id sid tid token lemma pos ajst-5438 1 1 academic academic ADJ ajst-5438 1 2 journal journal NOUN ajst-5438 1 3 of of ADP ajst-5438 1 4 science science NOUN ajst-5438 1 5 and and CCONJ ajst-5438 1 6 technology technology NOUN ajst-5438 1 7 issn issn NOUN ajst-5438 1 8 : : PUNCT ajst-5438 1 9 2771 2771 NUM ajst-5438 1 10 - - SYM ajst-5438 1 11 3032 3032 NUM ajst-5438 1 12 | | NOUN ajst-5438 1 13 vol vol NOUN ajst-5438 1 14 . . PROPN ajst-5438 2 1 5 5 NUM ajst-5438 2 2 , , PUNCT ajst-5438 2 3 no no INTJ ajst-5438 2 4 . . NOUN ajst-5438 2 5 1 1 NUM ajst-5438 2 6 , , PUNCT ajst-5438 2 7 2023 2023 NUM ajst-5438 2 8 112 112 NUM ajst-5438 2 9 research research NOUN ajst-5438 2 10 on on ADP ajst-5438 2 11 two‐stage two‐stage NOUN ajst-5438 2 12 estimation estimation NOUN ajst-5438 2 13 of of ADP ajst-5438 2 14 partially partially ADV ajst-5438 2 15 linear linear PROPN ajst-5438 2 16 single‐index single‐index NOUN ajst-5438 2 17 model model NOUN ajst-5438 2 18 with with ADP ajst-5438 2 19 longitudinal longitudinal ADJ ajst-5438 2 20 data datum NOUN ajst-5438 2 21 chaojie chaojie ADP ajst-5438 2 22 chang chang PROPN ajst-5438 2 23 school school PROPN ajst-5438 2 24 of of ADP ajst-5438 2 25 mathematics mathematic NOUN ajst-5438 2 26 and and CCONJ ajst-5438 2 27 science science NOUN ajst-5438 2 28 , , PUNCT ajst-5438 2 29 china china PROPN ajst-5438 2 30 university university PROPN ajst-5438 2 31 of of ADP ajst-5438 2 32 geosciences geoscience NOUN ajst-5438 2 33 ( ( PUNCT ajst-5438 2 34 wuhan wuhan PROPN ajst-5438 2 35 ) ) PUNCT ajst-5438 2 36 , , PUNCT ajst-5438 2 37 wuhan wuhan PROPN ajst-5438 2 38 , , PUNCT ajst-5438 2 39 china china PROPN ajst-5438 2 40 abstract abstract NOUN ajst-5438 2 41 : : PUNCT ajst-5438 2 42 partial partial ADJ ajst-5438 2 43 linear linear ADJ ajst-5438 2 44 single single ADJ ajst-5438 2 45 - - PUNCT ajst-5438 2 46 index index NOUN ajst-5438 2 47 model model NOUN ajst-5438 2 48 is be AUX ajst-5438 2 49 a a DET ajst-5438 2 50 kind kind NOUN ajst-5438 2 51 of of ADP ajst-5438 2 52 semi semi ADJ ajst-5438 2 53 - - ADJ ajst-5438 2 54 parametric parametric ADJ ajst-5438 2 55 model model NOUN ajst-5438 2 56 with with ADP ajst-5438 2 57 wide wide ADJ ajst-5438 2 58 application application NOUN ajst-5438 2 59 . . PUNCT ajst-5438 3 1 in in ADP ajst-5438 3 2 this this DET ajst-5438 3 3 paper paper NOUN ajst-5438 3 4 , , PUNCT ajst-5438 3 5 we we PRON ajst-5438 3 6 deal deal VERB ajst-5438 3 7 with with ADP ajst-5438 3 8 the the DET ajst-5438 3 9 partial partial ADJ ajst-5438 3 10 linear linear ADJ ajst-5438 3 11 single single ADJ ajst-5438 3 12 - - PUNCT ajst-5438 3 13 index index NOUN ajst-5438 3 14 model model NOUN ajst-5438 3 15 under under ADP ajst-5438 3 16 longitudinal longitudinal ADJ ajst-5438 3 17 data datum NOUN ajst-5438 3 18 . . PUNCT ajst-5438 4 1 a a DET ajst-5438 4 2 " " PUNCT ajst-5438 4 3 two two NUM ajst-5438 4 4 - - PUNCT ajst-5438 4 5 stage stage NOUN ajst-5438 4 6 estimation estimation NOUN ajst-5438 4 7 method method NOUN ajst-5438 4 8 " " PUNCT ajst-5438 4 9 without without ADP ajst-5438 4 10 iteration iteration NOUN ajst-5438 4 11 by by ADP ajst-5438 4 12 using use VERB ajst-5438 4 13 local local ADJ ajst-5438 4 14 polynomial polynomial ADJ ajst-5438 4 15 and and CCONJ ajst-5438 4 16 bias bias NOUN ajst-5438 4 17 correction correction NOUN ajst-5438 4 18 generalized generalize VERB ajst-5438 4 19 estimation estimation NOUN ajst-5438 4 20 equation equation NOUN ajst-5438 4 21 is be AUX ajst-5438 4 22 proposed propose VERB ajst-5438 4 23 . . PUNCT ajst-5438 5 1 under under ADP ajst-5438 5 2 some some DET ajst-5438 5 3 regularity regularity NOUN ajst-5438 5 4 conditions condition NOUN ajst-5438 5 5 , , PUNCT ajst-5438 5 6 the the DET ajst-5438 5 7 asymptotic asymptotic ADJ ajst-5438 5 8 properties property NOUN ajst-5438 5 9 of of ADP ajst-5438 5 10 the the DET ajst-5438 5 11 connection connection NOUN ajst-5438 5 12 function function NOUN ajst-5438 5 13 and and CCONJ ajst-5438 5 14 unknown unknown ADJ ajst-5438 5 15 parameter parameter NOUN ajst-5438 5 16 estimator estimator NOUN ajst-5438 5 17 are be AUX ajst-5438 5 18 investigated investigate VERB ajst-5438 5 19 . . PUNCT ajst-5438 6 1 numerical numerical PROPN ajst-5438 6 2 simulation simulation PROPN ajst-5438 6 3 shows show VERB ajst-5438 6 4 that that SCONJ ajst-5438 6 5 the the DET ajst-5438 6 6 proposed propose VERB ajst-5438 6 7 method method NOUN ajst-5438 6 8 is be AUX ajst-5438 6 9 robust robust ADJ ajst-5438 6 10 . . PUNCT ajst-5438 7 1 keywords keyword NOUN ajst-5438 7 2 : : PUNCT ajst-5438 7 3 partial partial ADJ ajst-5438 7 4 linear linear ADJ ajst-5438 7 5 single single ADJ ajst-5438 7 6 - - PUNCT ajst-5438 7 7 index index NOUN ajst-5438 7 8 model model NOUN ajst-5438 7 9 , , PUNCT ajst-5438 7 10 longitudinal longitudinal ADJ ajst-5438 7 11 data datum NOUN ajst-5438 7 12 , , PUNCT ajst-5438 7 13 local local ADJ ajst-5438 7 14 polynomial polynomial ADJ ajst-5438 7 15 , , PUNCT ajst-5438 7 16 generalized generalized ADJ ajst-5438 7 17 estimation estimation NOUN ajst-5438 7 18 equation equation NOUN ajst-5438 7 19 for for ADP ajst-5438 7 20 correcting correct VERB ajst-5438 7 21 deviation deviation NOUN ajst-5438 7 22 , , PUNCT ajst-5438 7 23 asymptotic asymptotic ADJ ajst-5438 7 24 normality normality NOUN ajst-5438 7 25 . . PUNCT ajst-5438 8 1 1 1 X ajst-5438 8 2 . . X ajst-5438 8 3 introduction introduction NOUN ajst-5438 8 4 this this DET ajst-5438 8 5 paper paper NOUN ajst-5438 8 6 studies study NOUN ajst-5438 8 7 the the DET ajst-5438 8 8 partial partial ADJ ajst-5438 8 9 linear linear ADJ ajst-5438 8 10 single single ADJ ajst-5438 8 11 - - PUNCT ajst-5438 8 12 indicator indicator NOUN ajst-5438 8 13 model model NOUN ajst-5438 8 14 under under ADP ajst-5438 8 15 the the DET ajst-5438 8 16 following follow VERB ajst-5438 8 17 longitudinal longitudinal ADJ ajst-5438 8 18 data datum NOUN ajst-5438 8 19 : : PUNCT ajst-5438 8 20 π‘Œ π‘Œ PROPN ajst-5438 8 21 𝑍 𝑍 VERB ajst-5438 8 22 πœƒ πœƒ NOUN ajst-5438 8 23 g g NOUN ajst-5438 8 24 𝑋 𝑋 PROPN ajst-5438 8 25 𝛽 𝛽 PROPN ajst-5438 8 26 πœ€ πœ€ PROPN ajst-5438 8 27 , , PUNCT ajst-5438 8 28 𝑖 𝑖 PROPN ajst-5438 8 29 1 1 NUM ajst-5438 8 30 , , PUNCT ajst-5438 8 31 β‹― β‹― NOUN ajst-5438 8 32 , , PUNCT ajst-5438 8 33 𝑛,𝑗 𝑛,𝑗 ADJ ajst-5438 8 34 1 1 NUM ajst-5438 8 35 , , PUNCT ajst-5438 8 36 β‹― β‹― PROPN ajst-5438 8 37 , , PUNCT ajst-5438 8 38 π‘š π‘š X ajst-5438 8 39 ( ( PUNCT ajst-5438 8 40 1 1 NUM ajst-5438 8 41 ) ) PUNCT ajst-5438 8 42 among among ADP ajst-5438 8 43 them they PRON ajst-5438 8 44 , , PUNCT ajst-5438 8 45 the the DET ajst-5438 8 46 explanatory explanatory ADJ ajst-5438 8 47 variables variable NOUN ajst-5438 8 48 𝑋 𝑋 NOUN ajst-5438 8 49 and and CCONJ ajst-5438 8 50 𝑍 𝑍 PROPN ajst-5438 8 51 are be AUX ajst-5438 8 52 related relate VERB ajst-5438 8 53 to to ADP ajst-5438 8 54 the the DET ajst-5438 8 55 model model NOUN ajst-5438 8 56 error error NOUN ajst-5438 8 57 πœ€ πœ€ NOUN ajst-5438 8 58 independent independent ADJ ajst-5438 8 59 from from ADP ajst-5438 8 60 each each DET ajst-5438 8 61 other other ADJ ajst-5438 8 62 . . PUNCT ajst-5438 9 1 g g PROPN ajst-5438 9 2 βˆ™ βˆ™ PROPN ajst-5438 9 3 is be AUX ajst-5438 9 4 a a DET ajst-5438 9 5 known know VERB ajst-5438 9 6 nonparametric nonparametric NOUN ajst-5438 9 7 connection connection NOUN ajst-5438 9 8 function function NOUN ajst-5438 9 9 , , PUNCT ajst-5438 9 10 𝛽 𝛽 NOUN ajst-5438 9 11 is be AUX ajst-5438 9 12 an an DET ajst-5438 9 13 unknown unknown ADJ ajst-5438 9 14 q q ADJ ajst-5438 9 15 - - PUNCT ajst-5438 9 16 dimension dimension NOUN ajst-5438 9 17 index index NOUN ajst-5438 9 18 parameter parameter NOUN ajst-5438 9 19 , , PUNCT ajst-5438 9 20 πœƒ πœƒ PROPN ajst-5438 9 21 is be AUX ajst-5438 9 22 an an DET ajst-5438 9 23 unknown unknown ADJ ajst-5438 9 24 pdimensional pdimensional ADJ ajst-5438 9 25 linear linear NOUN ajst-5438 9 26 parameter parameter NOUN ajst-5438 9 27 , , PUNCT ajst-5438 9 28 πœ€ πœ€ PROPN ajst-5438 9 29 is be AUX ajst-5438 9 30 the the DET ajst-5438 9 31 mean mean ADJ ajst-5438 9 32 value value NOUN ajst-5438 9 33 is be AUX ajst-5438 9 34 0 0 NUM ajst-5438 9 35 , , PUNCT ajst-5438 9 36 and and CCONJ ajst-5438 9 37 the the DET ajst-5438 9 38 variance variance NOUN ajst-5438 9 39 is be AUX ajst-5438 9 40 0 0 NUM ajst-5438 9 41 𝜎 𝜎 NUM ajst-5438 9 42 ∞ ∞ NUM ajst-5438 9 43 random random ADJ ajst-5438 9 44 error error NOUN ajst-5438 9 45 . . PUNCT ajst-5438 10 1 to to PART ajst-5438 10 2 ensure ensure VERB ajst-5438 10 3 the the DET ajst-5438 10 4 identifiability identifiability NOUN ajst-5438 10 5 of of ADP ajst-5438 10 6 the the DET ajst-5438 10 7 single single ADJ ajst-5438 10 8 indicator indicator NOUN ajst-5438 10 9 part part NOUN ajst-5438 10 10 , , PUNCT ajst-5438 10 11 suppose suppose VERB ajst-5438 10 12 ‖𝛽‖ ‖𝛽‖ PROPN ajst-5438 10 13 1 1 NUM ajst-5438 10 14 , , PUNCT ajst-5438 10 15 and and CCONJ ajst-5438 10 16 the the DET ajst-5438 10 17 first first ADJ ajst-5438 10 18 non non ADJ ajst-5438 10 19 - - ADJ ajst-5438 10 20 zero zero NUM ajst-5438 10 21 element element NOUN ajst-5438 10 22 of of ADP ajst-5438 10 23 the the DET ajst-5438 10 24 parameter parameter NOUN ajst-5438 10 25 vector vector NOUN ajst-5438 10 26 is be AUX ajst-5438 10 27 positive positive ADJ ajst-5438 10 28 . . PUNCT ajst-5438 11 1 in in ADP ajst-5438 11 2 this this DET ajst-5438 11 3 paper paper NOUN ajst-5438 11 4 , , PUNCT ajst-5438 11 5 under under ADP ajst-5438 11 6 the the DET ajst-5438 11 7 longitudinal longitudinal ADJ ajst-5438 11 8 data datum NOUN ajst-5438 11 9 , , PUNCT ajst-5438 11 10 each each DET ajst-5438 11 11 individual individual NOUN ajst-5438 11 12 is be AUX ajst-5438 11 13 observed observe VERB ajst-5438 11 14 for for ADP ajst-5438 11 15 a a DET ajst-5438 11 16 limited limited ADJ ajst-5438 11 17 number number NOUN ajst-5438 11 18 of of ADP ajst-5438 11 19 times time NOUN ajst-5438 11 20 , , PUNCT ajst-5438 11 21 namely namely ADV ajst-5438 11 22 π‘š π‘š ADP ajst-5438 11 23 𝑐 𝑐 NOUN ajst-5438 11 24 , , PUNCT ajst-5438 11 25 then then ADV ajst-5438 11 26 the the DET ajst-5438 11 27 total total ADJ ajst-5438 11 28 number number NOUN ajst-5438 11 29 of of ADP ajst-5438 11 30 observations observation NOUN ajst-5438 11 31 is be AUX ajst-5438 11 32 βˆ‘ βˆ‘ PROPN ajst-5438 11 33 π‘š π‘š PROPN ajst-5438 11 34 where where SCONJ ajst-5438 11 35 π‘š π‘š PROPN ajst-5438 11 36 is be AUX ajst-5438 11 37 a a DET ajst-5438 11 38 bounded bounded ADJ ajst-5438 11 39 positive positive ADJ ajst-5438 11 40 integer integer NOUN ajst-5438 11 41 sequence sequence NOUN ajst-5438 11 42 , , PUNCT ajst-5438 11 43 and and CCONJ ajst-5438 11 44 it it PRON ajst-5438 11 45 can can AUX ajst-5438 11 46 be be AUX ajst-5438 11 47 assumed assume VERB ajst-5438 11 48 that that SCONJ ajst-5438 11 49 𝑛 𝑛 PROPN ajst-5438 11 50 is be AUX ajst-5438 11 51 infinite infinite ADJ ajst-5438 11 52 , , PUNCT ajst-5438 11 53 which which PRON ajst-5438 11 54 means mean VERB ajst-5438 11 55 that that SCONJ ajst-5438 11 56 the the DET ajst-5438 11 57 total total ADJ ajst-5438 11 58 number number NOUN ajst-5438 11 59 of of ADP ajst-5438 11 60 observations observation NOUN ajst-5438 11 61 𝑁 𝑁 PROPN ajst-5438 11 62 and and CCONJ ajst-5438 11 63 the the DET ajst-5438 11 64 total total ADJ ajst-5438 11 65 number number NOUN ajst-5438 11 66 of of ADP ajst-5438 11 67 subjects subject NOUN ajst-5438 11 68 n n NUM ajst-5438 11 69 are be AUX ajst-5438 11 70 of of ADP ajst-5438 11 71 the the DET ajst-5438 11 72 same same ADJ ajst-5438 11 73 order order NOUN ajst-5438 11 74 , , PUNCT ajst-5438 11 75 that that ADV ajst-5438 11 76 is is ADV ajst-5438 11 77 , , PUNCT ajst-5438 11 78 𝑁 𝑁 PROPN ajst-5438 11 79 β†’ β†’ SYM ajst-5438 11 80 ∞ ∞ PROPN ajst-5438 11 81 and and CCONJ ajst-5438 11 82 𝑛 𝑛 PROPN ajst-5438 11 83 β†’ β†’ SYM ajst-5438 11 84 ∞ ∞ PROPN ajst-5438 11 85 are be AUX ajst-5438 11 86 equivalent equivalent ADJ ajst-5438 11 87 . . PUNCT ajst-5438 12 1 partial partial ADJ ajst-5438 12 2 linear linear ADJ ajst-5438 12 3 single single ADJ ajst-5438 12 4 - - PUNCT ajst-5438 12 5 indicator indicator NOUN ajst-5438 12 6 model model NOUN ajst-5438 12 7 is be AUX ajst-5438 12 8 the the DET ajst-5438 12 9 combination combination NOUN ajst-5438 12 10 of of ADP ajst-5438 12 11 linear linear ADJ ajst-5438 12 12 model model NOUN ajst-5438 12 13 and and CCONJ ajst-5438 12 14 single single ADJ ajst-5438 12 15 - - PUNCT ajst-5438 12 16 indicator indicator NOUN ajst-5438 12 17 model model NOUN ajst-5438 12 18 . . PUNCT ajst-5438 13 1 its its PRON ajst-5438 13 2 application application NOUN ajst-5438 13 3 range range NOUN ajst-5438 13 4 is be AUX ajst-5438 13 5 very very ADV ajst-5438 13 6 wide wide ADJ ajst-5438 13 7 , , PUNCT ajst-5438 13 8 which which PRON ajst-5438 13 9 has have AUX ajst-5438 13 10 aroused arouse VERB ajst-5438 13 11 the the DET ajst-5438 13 12 research research NOUN ajst-5438 13 13 interest interest NOUN ajst-5438 13 14 of of ADP ajst-5438 13 15 many many ADJ ajst-5438 13 16 scholars scholar NOUN ajst-5438 13 17 . . PUNCT ajst-5438 14 1 many many ADJ ajst-5438 14 2 methods method NOUN ajst-5438 14 3 have have AUX ajst-5438 14 4 been be AUX ajst-5438 14 5 proposed propose VERB ajst-5438 14 6 to to PART ajst-5438 14 7 estimate estimate VERB ajst-5438 14 8 unknown unknown ADJ ajst-5438 14 9 parameters parameter NOUN ajst-5438 14 10 and and CCONJ ajst-5438 14 11 non non ADJ ajst-5438 14 12 - - ADJ ajst-5438 14 13 parametric parametric ADJ ajst-5438 14 14 connection connection NOUN ajst-5438 14 15 functions[1 functions[1 NOUN ajst-5438 14 16 - - SYM ajst-5438 14 17 4 4 NUM ajst-5438 14 18 ] ] PUNCT ajst-5438 14 19 . . PUNCT ajst-5438 15 1 when when SCONJ ajst-5438 15 2 π‘ž π‘ž X ajst-5438 15 3 1 1 NUM ajst-5438 15 4 , , PUNCT ajst-5438 15 5 the the DET ajst-5438 15 6 model model NOUN ajst-5438 15 7 ( ( PUNCT ajst-5438 15 8 1 1 X ajst-5438 15 9 ) ) PUNCT ajst-5438 15 10 is be AUX ajst-5438 15 11 a a DET ajst-5438 15 12 partial partial ADJ ajst-5438 15 13 linear linear NOUN ajst-5438 15 14 model model NOUN ajst-5438 15 15 of of ADP ajst-5438 15 16 longitudinal longitudinal ADJ ajst-5438 15 17 data datum NOUN ajst-5438 15 18 [ [ X ajst-5438 15 19 5 5 NUM ajst-5438 15 20 - - SYM ajst-5438 15 21 6 6 NUM ajst-5438 15 22 ] ] PUNCT ajst-5438 15 23 ; ; PUNCT ajst-5438 15 24 when when SCONJ ajst-5438 15 25 𝑝 𝑝 PROPN ajst-5438 15 26 0 0 NUM ajst-5438 15 27 , , PUNCT ajst-5438 15 28 the the DET ajst-5438 15 29 model model NOUN ajst-5438 15 30 ( ( PUNCT ajst-5438 15 31 1 1 X ajst-5438 15 32 ) ) PUNCT ajst-5438 15 33 is be AUX ajst-5438 15 34 a a DET ajst-5438 15 35 single single ADJ ajst-5438 15 36 indicator indicator NOUN ajst-5438 15 37 model model NOUN ajst-5438 15 38 of of ADP ajst-5438 15 39 longitudinal longitudinal ADJ ajst-5438 15 40 data datum NOUN ajst-5438 15 41 [ [ X ajst-5438 15 42 7 7 NUM ajst-5438 15 43 - - SYM ajst-5438 15 44 8 8 NUM ajst-5438 15 45 ] ] PUNCT ajst-5438 15 46 ; ; PUNCT ajst-5438 15 47 when when SCONJ ajst-5438 15 48 g g PROPN ajst-5438 15 49 βˆ™ βˆ™ PROPN ajst-5438 15 50 selects select VERB ajst-5438 15 51 0 0 NUM ajst-5438 15 52 , , PUNCT ajst-5438 15 53 model model NOUN ajst-5438 15 54 ( ( PUNCT ajst-5438 15 55 1 1 NUM ajst-5438 15 56 ) ) PUNCT ajst-5438 15 57 is be AUX ajst-5438 15 58 a a DET ajst-5438 15 59 linear linear ADJ ajst-5438 15 60 regression regression NOUN ajst-5438 15 61 model model NOUN ajst-5438 15 62 of of ADP ajst-5438 15 63 longitudinal longitudinal ADJ ajst-5438 15 64 data datum NOUN ajst-5438 15 65 [ [ X ajst-5438 15 66 9 9 NUM ajst-5438 15 67 ] ] PUNCT ajst-5438 15 68 . . PUNCT ajst-5438 16 1 the the DET ajst-5438 16 2 existing exist VERB ajst-5438 16 3 estimates estimate NOUN ajst-5438 16 4 of of ADP ajst-5438 16 5 partial partial ADJ ajst-5438 16 6 linear linear ADJ ajst-5438 16 7 single single ADJ ajst-5438 16 8 - - PUNCT ajst-5438 16 9 indicator indicator NOUN ajst-5438 16 10 models model NOUN ajst-5438 16 11 are be AUX ajst-5438 16 12 mainly mainly ADV ajst-5438 16 13 based base VERB ajst-5438 16 14 on on ADP ajst-5438 16 15 the the DET ajst-5438 16 16 mean mean ADJ ajst-5438 16 17 regression regression NOUN ajst-5438 16 18 of of ADP ajst-5438 16 19 least least ADJ ajst-5438 16 20 squares square NOUN ajst-5438 16 21 or or CCONJ ajst-5438 16 22 likelihood likelihood NOUN ajst-5438 16 23 method method NOUN ajst-5438 16 24 , , PUNCT ajst-5438 16 25 and and CCONJ ajst-5438 16 26 the the DET ajst-5438 16 27 distribution distribution NOUN ajst-5438 16 28 of of ADP ajst-5438 16 29 random random ADJ ajst-5438 16 30 error error NOUN ajst-5438 16 31 needs need VERB ajst-5438 16 32 to to PART ajst-5438 16 33 be be AUX ajst-5438 16 34 assumed assume VERB ajst-5438 16 35 . . PUNCT ajst-5438 17 1 however however ADV ajst-5438 17 2 , , PUNCT ajst-5438 17 3 if if SCONJ ajst-5438 17 4 the the DET ajst-5438 17 5 assumption assumption NOUN ajst-5438 17 6 is be AUX ajst-5438 17 7 incorrect incorrect ADJ ajst-5438 17 8 , , PUNCT ajst-5438 17 9 the the DET ajst-5438 17 10 estimation estimation NOUN ajst-5438 17 11 results result NOUN ajst-5438 17 12 may may AUX ajst-5438 17 13 be be AUX ajst-5438 17 14 inaccurate inaccurate ADJ ajst-5438 17 15 or or CCONJ ajst-5438 17 16 even even ADV ajst-5438 17 17 wrong wrong ADJ ajst-5438 17 18 , , PUNCT ajst-5438 17 19 and and CCONJ ajst-5438 17 20 the the DET ajst-5438 17 21 research research NOUN ajst-5438 17 22 work work NOUN ajst-5438 17 23 will will AUX ajst-5438 17 24 be be AUX ajst-5438 17 25 meaningless meaningless ADJ ajst-5438 17 26 . . PUNCT ajst-5438 18 1 in in ADP ajst-5438 18 2 addition addition NOUN ajst-5438 18 3 , , PUNCT ajst-5438 18 4 at at ADP ajst-5438 18 5 present present ADJ ajst-5438 18 6 , , PUNCT ajst-5438 18 7 the the DET ajst-5438 18 8 linear linear ADJ ajst-5438 18 9 parameters parameter NOUN ajst-5438 18 10 in in ADP ajst-5438 18 11 the the DET ajst-5438 18 12 model model NOUN ajst-5438 18 13 πœƒ πœƒ NOUN ajst-5438 18 14 and and CCONJ ajst-5438 18 15 index index NOUN ajst-5438 18 16 parameters parameter NOUN ajst-5438 18 17 𝛽 𝛽 NOUN ajst-5438 18 18 is be AUX ajst-5438 18 19 almost almost ADV ajst-5438 18 20 estimated estimate VERB ajst-5438 18 21 at at ADP ajst-5438 18 22 the the DET ajst-5438 18 23 same same ADJ ajst-5438 18 24 time time NOUN ajst-5438 18 25 , , PUNCT ajst-5438 18 26 and and CCONJ ajst-5438 18 27 requires require VERB ajst-5438 18 28 multiple multiple ADJ ajst-5438 18 29 iterations iteration NOUN ajst-5438 18 30 . . PUNCT ajst-5438 19 1 the the DET ajst-5438 19 2 calculation calculation NOUN ajst-5438 19 3 is be AUX ajst-5438 19 4 very very ADV ajst-5438 19 5 complex complex ADJ ajst-5438 19 6 and and CCONJ ajst-5438 19 7 time time NOUN ajst-5438 19 8 - - PUNCT ajst-5438 19 9 consuming consume VERB ajst-5438 19 10 . . PUNCT ajst-5438 20 1 then then ADV ajst-5438 20 2 , , PUNCT ajst-5438 20 3 due due ADP ajst-5438 20 4 to to ADP ajst-5438 20 5 𝛽 𝛽 NOUN ajst-5438 20 6 and and CCONJ ajst-5438 20 7 πœƒ πœƒ NOUN ajst-5438 20 8 may may AUX ajst-5438 20 9 have have VERB ajst-5438 20 10 some some DET ajst-5438 20 11 correlation correlation NOUN ajst-5438 20 12 , , PUNCT ajst-5438 20 13 which which PRON ajst-5438 20 14 may may AUX ajst-5438 20 15 cause cause VERB ajst-5438 20 16 𝛽 𝛽 NOUN ajst-5438 20 17 is be AUX ajst-5438 20 18 difficult difficult ADJ ajst-5438 20 19 to to PART ajst-5438 20 20 identify identify VERB ajst-5438 20 21 , , PUNCT ajst-5438 20 22 which which PRON ajst-5438 20 23 will will AUX ajst-5438 20 24 also also ADV ajst-5438 20 25 lead lead VERB ajst-5438 20 26 to to ADP ajst-5438 20 27 inaccurate inaccurate ADJ ajst-5438 20 28 estimation estimation NOUN ajst-5438 20 29 results result NOUN ajst-5438 20 30 . . PUNCT ajst-5438 21 1 in in ADP ajst-5438 21 2 view view NOUN ajst-5438 21 3 of of ADP ajst-5438 21 4 the the DET ajst-5438 21 5 above above ADJ ajst-5438 21 6 problems problem NOUN ajst-5438 21 7 , , PUNCT ajst-5438 21 8 without without ADP ajst-5438 21 9 considering consider VERB ajst-5438 21 10 the the DET ajst-5438 21 11 intra intra ADJ ajst-5438 21 12 - - ADJ ajst-5438 21 13 group group NOUN ajst-5438 21 14 correlation correlation NOUN ajst-5438 21 15 , , PUNCT ajst-5438 21 16 this this DET ajst-5438 21 17 paper paper NOUN ajst-5438 21 18 proposes propose VERB ajst-5438 21 19 a a DET ajst-5438 21 20 " " PUNCT ajst-5438 21 21 two two NUM ajst-5438 21 22 - - PUNCT ajst-5438 21 23 stage stage NOUN ajst-5438 21 24 estimation estimation NOUN ajst-5438 21 25 method method NOUN ajst-5438 21 26 " " PUNCT ajst-5438 21 27 without without ADP ajst-5438 21 28 iteration iteration NOUN ajst-5438 21 29 based base VERB ajst-5438 21 30 on on ADP ajst-5438 21 31 local local ADJ ajst-5438 21 32 polynomial polynomial ADJ ajst-5438 21 33 estimation estimation NOUN ajst-5438 21 34 and and CCONJ ajst-5438 21 35 bias bias NOUN ajst-5438 21 36 correction correction NOUN ajst-5438 21 37 generalized generalize VERB ajst-5438 21 38 estimation estimation NOUN ajst-5438 21 39 equation equation NOUN ajst-5438 21 40 𝛽 𝛽 PROPN ajst-5438 21 41 and and CCONJ ajst-5438 21 42 linear linear PROPN ajst-5438 21 43 parameters parameter NOUN ajst-5438 21 44 πœƒ πœƒ NUM ajst-5438 21 45 this this DET ajst-5438 21 46 method method NOUN ajst-5438 21 47 can can AUX ajst-5438 21 48 reduce reduce VERB ajst-5438 21 49 the the DET ajst-5438 21 50 running running NOUN ajst-5438 21 51 time time NOUN ajst-5438 21 52 and and CCONJ ajst-5438 21 53 improve improve VERB ajst-5438 21 54 the the DET ajst-5438 21 55 operation operation NOUN ajst-5438 21 56 efficiency efficiency NOUN ajst-5438 21 57 . . PUNCT ajst-5438 22 1 in in ADP ajst-5438 22 2 addition addition NOUN ajst-5438 22 3 , , PUNCT ajst-5438 22 4 in in ADP ajst-5438 22 5 order order NOUN ajst-5438 22 6 to to PART ajst-5438 22 7 solve solve VERB ajst-5438 22 8 𝛽 𝛽 NOUN ajst-5438 22 9 and and CCONJ ajst-5438 22 10 πœƒ πœƒ NOUN ajst-5438 22 11 for for ADP ajst-5438 22 12 the the DET ajst-5438 22 13 linear linear ADJ ajst-5438 22 14 correlation correlation NOUN ajst-5438 22 15 between between ADP ajst-5438 22 16 𝑋 𝑋 PROPN ajst-5438 22 17 and and CCONJ ajst-5438 22 18 𝑍 𝑍 PROPN ajst-5438 22 19 , , PUNCT ajst-5438 22 20 the the DET ajst-5438 22 21 formula formula NOUN ajst-5438 22 22 ( ( PUNCT ajst-5438 22 23 2 2 X ajst-5438 22 24 ) ) PUNCT ajst-5438 22 25 is be AUX ajst-5438 22 26 introduced introduce VERB ajst-5438 22 27 to to PART ajst-5438 22 28 eliminate eliminate VERB ajst-5438 22 29 the the DET ajst-5438 22 30 correlation correlation NOUN ajst-5438 22 31 between between ADP ajst-5438 22 32 x x PROPN ajst-5438 22 33 and and CCONJ ajst-5438 22 34 z z NOUN ajst-5438 22 35 , , PUNCT ajst-5438 22 36 so so SCONJ ajst-5438 22 37 as as SCONJ ajst-5438 22 38 to to PART ajst-5438 22 39 improve improve VERB ajst-5438 22 40 the the DET ajst-5438 22 41 accuracy accuracy NOUN ajst-5438 22 42 of of ADP ajst-5438 22 43 parameter parameter NOUN ajst-5438 22 44 estimation estimation NOUN ajst-5438 22 45 . . PUNCT ajst-5438 23 1 in in ADP ajst-5438 23 2 section section NOUN ajst-5438 23 3 1 1 NUM ajst-5438 23 4 , , PUNCT ajst-5438 23 5 we we PRON ajst-5438 23 6 give give VERB ajst-5438 23 7 a a DET ajst-5438 23 8 " " PUNCT ajst-5438 23 9 two two NUM ajst-5438 23 10 - - PUNCT ajst-5438 23 11 stage stage NOUN ajst-5438 23 12 estimation estimation NOUN ajst-5438 23 13 method method NOUN ajst-5438 23 14 " " PUNCT ajst-5438 23 15 without without ADP ajst-5438 23 16 iteration iteration NOUN ajst-5438 23 17 based base VERB ajst-5438 23 18 on on ADP ajst-5438 23 19 local local ADJ ajst-5438 23 20 polynomial polynomial ADJ ajst-5438 23 21 estimation estimation NOUN ajst-5438 23 22 and and CCONJ ajst-5438 23 23 bias bias NOUN ajst-5438 23 24 correction correction NOUN ajst-5438 23 25 generalized generalize VERB ajst-5438 23 26 estimation estimation NOUN ajst-5438 23 27 equation equation NOUN ajst-5438 23 28 [ [ X ajst-5438 23 29 10 10 NUM ajst-5438 23 30 ] ] PUNCT ajst-5438 23 31 . . PUNCT ajst-5438 24 1 in in ADP ajst-5438 24 2 section section NOUN ajst-5438 24 3 2 2 NUM ajst-5438 24 4 , , PUNCT ajst-5438 24 5 we we PRON ajst-5438 24 6 study study VERB ajst-5438 24 7 the the DET ajst-5438 24 8 index index NOUN ajst-5438 24 9 parameters parameter NOUN ajst-5438 24 10 under under ADP ajst-5438 24 11 some some DET ajst-5438 24 12 regularity regularity NOUN ajst-5438 24 13 assumptions assumption NOUN ajst-5438 24 14 Ξ² Ξ² X ajst-5438 24 15 and and CCONJ ajst-5438 24 16 linear linear PROPN ajst-5438 24 17 parameters parameter NOUN ajst-5438 24 18 ΞΈ ΞΈ VERB ajst-5438 24 19 the the DET ajst-5438 24 20 asymptotic asymptotic ADJ ajst-5438 24 21 normality normality NOUN ajst-5438 24 22 of of ADP ajst-5438 24 23 the the DET ajst-5438 24 24 estimator estimator NOUN ajst-5438 24 25 and and CCONJ ajst-5438 24 26 the the DET ajst-5438 24 27 asymptotic asymptotic ADJ ajst-5438 24 28 normality normality NOUN ajst-5438 24 29 of of ADP ajst-5438 24 30 the the DET ajst-5438 24 31 estimator estimator NOUN ajst-5438 24 32 of of ADP ajst-5438 24 33 the the DET ajst-5438 24 34 connection connection NOUN ajst-5438 24 35 function function NOUN ajst-5438 24 36 g g PROPN ajst-5438 24 37 βˆ™ βˆ™ PROPN ajst-5438 24 38 . . PUNCT ajst-5438 25 1 the the DET ajst-5438 25 2 random random ADJ ajst-5438 25 3 simulation simulation NOUN ajst-5438 25 4 experiment experiment NOUN ajst-5438 25 5 in in ADP ajst-5438 25 6 section section NOUN ajst-5438 25 7 3 3 NUM ajst-5438 25 8 shows show VERB ajst-5438 25 9 that that SCONJ ajst-5438 25 10 the the DET ajst-5438 25 11 estimator estimator NOUN ajst-5438 25 12 obtained obtain VERB ajst-5438 25 13 by by ADP ajst-5438 25 14 this this DET ajst-5438 25 15 method method NOUN ajst-5438 25 16 is be AUX ajst-5438 25 17 robust robust ADJ ajst-5438 25 18 . . PUNCT ajst-5438 26 1 assume assume VERB ajst-5438 26 2 that that SCONJ ajst-5438 26 3 the the DET ajst-5438 26 4 observation observation NOUN ajst-5438 26 5 value value NOUN ajst-5438 26 6 is be AUX ajst-5438 26 7 𝑋 𝑋 PROPN ajst-5438 26 8 , , PUNCT ajst-5438 26 9 π‘Œ π‘Œ PROPN ajst-5438 26 10 , , PUNCT ajst-5438 26 11 𝑍 𝑍 NOUN ajst-5438 26 12 ; ; PUNCT ajst-5438 26 13 𝑖 𝑖 SYM ajst-5438 26 14 1 1 NUM ajst-5438 26 15 , , PUNCT ajst-5438 26 16 β‹― β‹― NOUN ajst-5438 26 17 , , PUNCT ajst-5438 26 18 𝑛,𝑗 𝑛,𝑗 ADJ ajst-5438 26 19 1 1 NUM ajst-5438 26 20 , , PUNCT ajst-5438 26 21 β‹― β‹― PROPN ajst-5438 26 22 , , PUNCT ajst-5438 26 23 π‘š π‘š PROPN ajst-5438 26 24 from from ADP ajst-5438 26 25 the the DET ajst-5438 26 26 sample sample NOUN ajst-5438 26 27 of of ADP ajst-5438 26 28 model model NOUN ajst-5438 26 29 ( ( PUNCT ajst-5438 26 30 1 1 NUM ajst-5438 26 31 ) ) PUNCT ajst-5438 26 32 . . PUNCT ajst-5438 27 1 for for ADP ajst-5438 27 2 the the DET ajst-5438 27 3 convenience convenience NOUN ajst-5438 27 4 of of ADP ajst-5438 27 5 calculation calculation NOUN ajst-5438 27 6 ： ： PUNCT ajst-5438 27 7 π‘Œ π‘Œ PROPN ajst-5438 27 8 𝑦 𝑦 PRON ajst-5438 27 9 , , PUNCT ajst-5438 27 10 β‹― β‹― PROPN ajst-5438 27 11 , , PUNCT ajst-5438 27 12 𝑦 𝑦 NOUN ajst-5438 27 13 , , PUNCT ajst-5438 27 14 𝑋 𝑋 PROPN ajst-5438 27 15 π‘₯ π‘₯ PROPN ajst-5438 27 16 , , PUNCT ajst-5438 27 17 β‹― β‹― PROPN ajst-5438 27 18 , , PUNCT ajst-5438 27 19 π‘₯ π‘₯ PROPN ajst-5438 27 20 𝑍 𝑍 VERB ajst-5438 27 21 𝑧 𝑧 PRON ajst-5438 27 22 , , PUNCT ajst-5438 27 23 β‹― β‹― PROPN ajst-5438 27 24 , , PUNCT ajst-5438 27 25 𝑧 𝑧 X ajst-5438 27 26 , , PUNCT ajst-5438 27 27 πœ€ πœ€ PROPN ajst-5438 27 28 πœ€ πœ€ PROPN ajst-5438 27 29 , , PUNCT ajst-5438 27 30 β‹― β‹― PROPN ajst-5438 27 31 , , PUNCT ajst-5438 27 32 πœ€ πœ€ PROPN ajst-5438 27 33 then then ADV ajst-5438 27 34 the the DET ajst-5438 27 35 model model NOUN ajst-5438 27 36 ( ( PUNCT ajst-5438 27 37 1 1 X ajst-5438 27 38 ) ) PUNCT ajst-5438 27 39 can can AUX ajst-5438 27 40 be be AUX ajst-5438 27 41 written write VERB ajst-5438 27 42 as as ADP ajst-5438 27 43 the the DET ajst-5438 27 44 following follow VERB ajst-5438 27 45 vector vector NOUN ajst-5438 27 46 matrix matrix NOUN ajst-5438 27 47 form form NOUN ajst-5438 27 48 : : PUNCT ajst-5438 27 49 π‘Œ π‘Œ PROPN ajst-5438 27 50 𝑍 𝑍 VERB ajst-5438 27 51 πœƒ πœƒ NOUN ajst-5438 27 52 𝑔 𝑔 NOUN ajst-5438 27 53 𝑋 𝑋 PROPN ajst-5438 27 54 𝛽 𝛽 PROPN ajst-5438 27 55 πœ€ πœ€ PROPN ajst-5438 27 56 , , PUNCT ajst-5438 27 57 𝑖 𝑖 PROPN ajst-5438 27 58 1 1 NUM ajst-5438 27 59 , , PUNCT ajst-5438 27 60 β‹― β‹― PROPN ajst-5438 27 61 , , PUNCT ajst-5438 27 62 𝑛 𝑛 PRON ajst-5438 27 63 to to PART ajst-5438 27 64 ensure ensure VERB ajst-5438 27 65 the the DET ajst-5438 27 66 identifiability identifiability NOUN ajst-5438 27 67 of of ADP ajst-5438 27 68 the the DET ajst-5438 27 69 model model NOUN ajst-5438 27 70 , , PUNCT ajst-5438 27 71 it it PRON ajst-5438 27 72 is be AUX ajst-5438 27 73 assumed assume VERB ajst-5438 27 74 that that SCONJ ajst-5438 27 75 𝛽 𝛽 PROPN ajst-5438 27 76 1,𝛽 1,𝛽 NUM ajst-5438 27 77 , , PUNCT ajst-5438 27 78 β‹― β‹― PROPN ajst-5438 27 79 , , PUNCT ajst-5438 27 80 𝛽 𝛽 PROPN ajst-5438 27 81 . . PUNCT ajst-5438 28 1 in in ADP ajst-5438 28 2 order order NOUN ajst-5438 28 3 not not PART ajst-5438 28 4 to to PART ajst-5438 28 5 lose lose VERB ajst-5438 28 6 generality generality NOUN ajst-5438 28 7 , , PUNCT ajst-5438 28 8 real real ADJ ajst-5438 28 9 parameters parameter NOUN ajst-5438 28 10 are be AUX ajst-5438 28 11 assumed assume VERB ajst-5438 28 12 𝛽 𝛽 NOUN ajst-5438 28 13 is be AUX ajst-5438 28 14 a a DET ajst-5438 28 15 positive positive ADJ ajst-5438 28 16 definite definite ADJ ajst-5438 28 17 matrix matrix NOUN ajst-5438 28 18 . . PUNCT ajst-5438 29 1 in in ADP ajst-5438 29 2 addition addition NOUN ajst-5438 29 3 , , PUNCT ajst-5438 29 4 based base VERB ajst-5438 29 5 on on ADP ajst-5438 29 6 the the DET ajst-5438 29 7 linear linear ADJ ajst-5438 29 8 correlation correlation NOUN ajst-5438 29 9 between between ADP ajst-5438 29 10 𝑋 𝑋 PROPN ajst-5438 29 11 and and CCONJ ajst-5438 29 12 𝑍,let 𝑍,let PROPN ajst-5438 29 13 𝑍 𝑍 VERB ajst-5438 29 14 πœ‘ πœ‘ NOUN ajst-5438 29 15 𝑋 𝑋 PROPN ajst-5438 29 16 𝛽 𝛽 PROPN ajst-5438 29 17 πœ‚ πœ‚ PROPN ajst-5438 29 18 ( ( PUNCT ajst-5438 29 19 2 2 NUM ajst-5438 29 20 ) ) PUNCT ajst-5438 29 21 here here ADV ajst-5438 29 22 πœ‘ πœ‘ X ajst-5438 29 23 βˆ™ βˆ™ PROPN ajst-5438 29 24 is be AUX ajst-5438 29 25 an an DET ajst-5438 29 26 unknown unknown ADJ ajst-5438 29 27 function function NOUN ajst-5438 29 28 from from ADP ajst-5438 29 29 𝑅 𝑅 PROPN ajst-5438 29 30 to to ADP ajst-5438 29 31 𝑅 𝑅 PROPN ajst-5438 29 32 , , PUNCT ajst-5438 29 33 𝛽 𝛽 PROPN ajst-5438 29 34 is be AUX ajst-5438 29 35 a a DET ajst-5438 29 36 𝑝 𝑝 PROPN ajst-5438 29 37 𝑑 𝑑 PRON ajst-5438 29 38 with with ADP ajst-5438 29 39 standard standard ADJ ajst-5438 29 40 orthogonal orthogonal ADJ ajst-5438 29 41 columns column NOUN ajst-5438 29 42 matrix matrix NOUN ajst-5438 29 43 , , PUNCT ajst-5438 29 44 πœ‚ πœ‚ NOUN ajst-5438 29 45 the the DET ajst-5438 29 46 mean mean ADJ ajst-5438 29 47 value value NOUN ajst-5438 29 48 of of ADP ajst-5438 29 49 is be AUX ajst-5438 29 50 zero zero NUM ajst-5438 29 51 and and CCONJ ajst-5438 29 52 is be AUX ajst-5438 29 53 independent independent ADJ ajst-5438 29 54 of of ADP ajst-5438 29 55 𝑋. 𝑋. PROPN ajst-5438 29 56 the the DET ajst-5438 29 57 dimension dimension NOUN ajst-5438 29 58 𝑑 𝑑 NOUN ajst-5438 29 59 is be AUX ajst-5438 29 60 usually usually ADV ajst-5438 29 61 much much ADV ajst-5438 29 62 smaller small ADJ ajst-5438 29 63 than than ADP ajst-5438 29 64 the the DET ajst-5438 29 65 dimension dimension NOUN ajst-5438 29 66 𝑝 𝑝 PROPN ajst-5438 29 67 of of ADP ajst-5438 29 68 𝑋 𝑋 PROPN ajst-5438 29 69 , , PUNCT ajst-5438 29 70 113 113 NUM ajst-5438 29 71 which which PRON ajst-5438 29 72 is be AUX ajst-5438 29 73 a a DET ajst-5438 29 74 common common ADJ ajst-5438 29 75 dimensionality dimensionality NOUN ajst-5438 29 76 reduction reduction NOUN ajst-5438 29 77 assumption assumption NOUN ajst-5438 29 78 in in ADP ajst-5438 29 79 the the DET ajst-5438 29 80 literature literature NOUN ajst-5438 29 81 . . PUNCT ajst-5438 30 1 in in ADP ajst-5438 30 2 this this DET ajst-5438 30 3 chapter chapter NOUN ajst-5438 30 4 , , PUNCT ajst-5438 30 5 we we PRON ajst-5438 30 6 conduct conduct VERB ajst-5438 30 7 statistical statistical ADJ ajst-5438 30 8 inference inference NOUN ajst-5438 30 9 research research NOUN ajst-5438 30 10 under under ADP ajst-5438 30 11 the the DET ajst-5438 30 12 condition condition NOUN ajst-5438 30 13 of of ADP ajst-5438 30 14 𝑑 𝑑 PROPN ajst-5438 30 15 1 1 NUM ajst-5438 30 16 . . PUNCT ajst-5438 31 1 generally generally ADV ajst-5438 31 2 , , PUNCT ajst-5438 31 3 once once SCONJ ajst-5438 31 4 you you PRON ajst-5438 31 5 get get VERB ajst-5438 31 6 𝛽 𝛽 NOUN ajst-5438 31 7 the the DET ajst-5438 31 8 βˆšπ‘› βˆšπ‘› NOUN ajst-5438 31 9 of of ADP ajst-5438 31 10 is be AUX ajst-5438 31 11 estimated estimate VERB ajst-5438 31 12 and and CCONJ ajst-5438 31 13 inserted insert VERB ajst-5438 31 14 ( ( PUNCT ajst-5438 31 15 1 1 NUM ajst-5438 31 16 ) ) PUNCT ajst-5438 31 17 , , PUNCT ajst-5438 31 18 and and CCONJ ajst-5438 31 19 the the DET ajst-5438 31 20 best good ADJ ajst-5438 31 21 estimate estimate NOUN ajst-5438 31 22 can can AUX ajst-5438 31 23 be be AUX ajst-5438 31 24 achieved achieve VERB ajst-5438 31 25 by by ADP ajst-5438 31 26 the the DET ajst-5438 31 27 method method NOUN ajst-5438 31 28 developed develop VERB ajst-5438 31 29 for for ADP ajst-5438 31 30 the the DET ajst-5438 31 31 partial partial ADJ ajst-5438 31 32 linear linear PROPN ajst-5438 31 33 model model NOUN ajst-5438 32 1 πœƒ πœƒ NOUN ajst-5438 32 2 , , PUNCT ajst-5438 32 3 however however ADV ajst-5438 32 4 , , PUNCT ajst-5438 32 5 𝛽 𝛽 PROPN ajst-5438 32 6 and and CCONJ ajst-5438 32 7 πœƒ πœƒ PRON ajst-5438 32 8 may may AUX ajst-5438 32 9 be be AUX ajst-5438 32 10 related relate VERB ajst-5438 32 11 , , PUNCT ajst-5438 32 12 causing cause VERB ajst-5438 32 13 𝛽 𝛽 NOUN ajst-5438 32 14 is be AUX ajst-5438 32 15 difficult difficult ADJ ajst-5438 32 16 to to PART ajst-5438 32 17 identify identify VERB ajst-5438 32 18 . . PUNCT ajst-5438 33 1 this this PRON ajst-5438 33 2 is be AUX ajst-5438 33 3 the the DET ajst-5438 33 4 advantage advantage NOUN ajst-5438 33 5 of of ADP ajst-5438 33 6 introducing introduce VERB ajst-5438 33 7 model model NOUN ajst-5438 33 8 assumption assumption NOUN ajst-5438 33 9 ( ( PUNCT ajst-5438 33 10 2 2 NUM ajst-5438 33 11 ) ) PUNCT ajst-5438 33 12 , , PUNCT ajst-5438 33 13 because because SCONJ ajst-5438 33 14 it it PRON ajst-5438 33 15 allows allow VERB ajst-5438 33 16 deleting delete VERB ajst-5438 33 17 the the DET ajst-5438 33 18 𝑍 𝑍 PROPN ajst-5438 33 19 part part NOUN ajst-5438 33 20 related relate VERB ajst-5438 33 21 to to ADP ajst-5438 33 22 𝑋 𝑋 PROPN ajst-5438 33 23 , , PUNCT ajst-5438 33 24 so so SCONJ ajst-5438 33 25 that that SCONJ ajst-5438 33 26 the the DET ajst-5438 33 27 residual residual ADJ ajst-5438 33 28 in in ADP ajst-5438 33 29 ( ( PUNCT ajst-5438 33 30 2 2 NUM ajst-5438 33 31 ) ) PUNCT ajst-5438 33 32 πœ‚ πœ‚ NOUN ajst-5438 33 33 will will AUX ajst-5438 33 34 be be AUX ajst-5438 33 35 independent independent ADJ ajst-5438 33 36 of of ADP ajst-5438 33 37 𝑋 𝑋 PROPN ajst-5438 33 38 . . PUNCT ajst-5438 34 1 similarly similarly ADV ajst-5438 34 2 , , PUNCT ajst-5438 34 3 it it PRON ajst-5438 34 4 is be AUX ajst-5438 34 5 necessary necessary ADJ ajst-5438 34 6 to to PART ajst-5438 34 7 add add VERB ajst-5438 34 8 an an DET ajst-5438 34 9 identifiability identifiability NOUN ajst-5438 34 10 condition condition NOUN ajst-5438 34 11 , , PUNCT ajst-5438 34 12 i.e. i.e. X ajst-5438 34 13 ‖𝛽 ‖𝛽 PUNCT ajst-5438 34 14 β€– β€– ADJ ajst-5438 34 15 1 1 NUM ajst-5438 34 16 and and CCONJ ajst-5438 34 17 the the DET ajst-5438 34 18 first first ADJ ajst-5438 34 19 component component NOUN ajst-5438 34 20 of of ADP ajst-5438 34 21 the the DET ajst-5438 34 22 parameter parameter NOUN ajst-5438 34 23 is be AUX ajst-5438 34 24 positive positive ADJ ajst-5438 34 25 . . PUNCT ajst-5438 35 1 the the DET ajst-5438 35 2 parameter parameter NOUN ajst-5438 35 3 vector vector NOUN ajst-5438 35 4 is be AUX ajst-5438 35 5 given give VERB ajst-5438 35 6 below below ADP ajst-5438 35 7 𝛽 𝛽 NOUN ajst-5438 35 8 and and CCONJ ajst-5438 35 9 πœƒ πœƒ NOUN ajst-5438 35 10 and and CCONJ ajst-5438 35 11 connection connection NOUN ajst-5438 35 12 function function NOUN ajst-5438 35 13 g g PROPN ajst-5438 35 14 βˆ™ βˆ™ PROPN ajst-5438 35 15 the the DET ajst-5438 35 16 estimation estimation NOUN ajst-5438 35 17 algorithm algorithm NOUN ajst-5438 35 18 of of ADP ajst-5438 35 19 " " PUNCT ajst-5438 35 20 twostage twostage NOUN ajst-5438 35 21 estimation estimation NOUN ajst-5438 35 22 method method NOUN ajst-5438 35 23 " " PUNCT ajst-5438 35 24 : : PUNCT ajst-5438 35 25 algorithm algorithm NOUN ajst-5438 35 26 for for ADP ajst-5438 35 27 stage stage NOUN ajst-5438 35 28 one one NUM ajst-5438 35 29 : : PUNCT ajst-5438 35 30 1 1 NUM ajst-5438 35 31 . . X ajst-5438 35 32 first first ADV ajst-5438 35 33 , , PUNCT ajst-5438 35 34 construct construct VERB ajst-5438 35 35 a a DET ajst-5438 35 36 regression regression NOUN ajst-5438 35 37 model model NOUN ajst-5438 35 38 𝑍 𝑍 NOUN ajst-5438 35 39 and and CCONJ ajst-5438 35 40 𝑋 𝑋 NOUN ajst-5438 35 41 is be AUX ajst-5438 35 42 regressed regress VERB ajst-5438 35 43 to to PART ajst-5438 35 44 obtain obtain VERB ajst-5438 35 45 𝛽 𝛽 DET ajst-5438 35 46 estimator estimator NOUN ajst-5438 35 47 of of ADP ajst-5438 35 48 𝛽 𝛽 NOUN ajst-5438 35 49 2 2 NUM ajst-5438 35 50 . . PUNCT ajst-5438 35 51 using use VERB ajst-5438 35 52 local local ADJ ajst-5438 35 53 smoothing smooth VERB ajst-5438 35 54 estimation estimation NOUN ajst-5438 35 55 to to PART ajst-5438 35 56 get get VERB ajst-5438 35 57 οΏ½ οΏ½ NOUN ajst-5438 35 58 Μ‚ Μ‚ VERB ajst-5438 35 59 οΏ½ οΏ½ NOUN ajst-5438 35 60 𝑍 𝑍 VERB ajst-5438 35 61 πœ‘ πœ‘ NOUN ajst-5438 35 62 𝑋 𝑋 PROPN ajst-5438 35 63 𝛽 𝛽 PROPN ajst-5438 35 64 , , PUNCT ajst-5438 35 65 so so ADV ajst-5438 35 66 π‘Œ π‘Œ PROPN ajst-5438 35 67 οΏ½ οΏ½ PROPN ajst-5438 35 68 Μ‚ Μ‚ VERB ajst-5438 35 69 οΏ½ οΏ½ NOUN ajst-5438 35 70 πœƒ πœƒ NUM ajst-5438 35 71 β„Ž β„Ž ADP ajst-5438 35 72 𝑋 𝑋 PROPN ajst-5438 35 73 𝛽 𝛽 PROPN ajst-5438 35 74 𝑋 𝑋 PROPN ajst-5438 35 75 𝛽 𝛽 PROPN ajst-5438 35 76 πœ€ πœ€ PROPN ajst-5438 35 77 , , PUNCT ajst-5438 35 78 her her PRON ajst-5438 35 79 πœ‚ πœ‚ NOUN ajst-5438 35 80 and and CCONJ ajst-5438 35 81 𝑋 𝑋 PROPN ajst-5438 35 82 are be AUX ajst-5438 35 83 independent independent ADJ ajst-5438 35 84 of of ADP ajst-5438 35 85 each each DET ajst-5438 35 86 other other ADJ ajst-5438 35 87 . . PUNCT ajst-5438 36 1 3 3 X ajst-5438 36 2 . . X ajst-5438 36 3 for for ADP ajst-5438 36 4 π‘Œ π‘Œ PROPN ajst-5438 36 5 and and CCONJ ajst-5438 36 6 οΏ½ οΏ½ PROPN ajst-5438 36 7 Μ‚ Μ‚ VERB ajst-5438 36 8 οΏ½ οΏ½ PROPN ajst-5438 36 9 carries carry VERB ajst-5438 36 10 out out ADP ajst-5438 36 11 linear linear ADJ ajst-5438 36 12 regression regression NOUN ajst-5438 36 13 to to PART ajst-5438 36 14 obtain obtain VERB ajst-5438 36 15 πœƒ πœƒ PRON ajst-5438 36 16 initial initial ADJ ajst-5438 36 17 estimate estimate NOUN ajst-5438 36 18 of of ADP ajst-5438 36 19 πœƒ πœƒ NOUN ajst-5438 36 20 4 4 X ajst-5438 36 21 . . PUNCT ajst-5438 36 22 construct construct VERB ajst-5438 36 23 a a DET ajst-5438 36 24 regression regression NOUN ajst-5438 36 25 model model NOUN ajst-5438 36 26 π‘Œ π‘Œ PROPN ajst-5438 36 27 𝑍 𝑍 VERB ajst-5438 36 28 πœƒ πœƒ NOUN ajst-5438 36 29 与 与 NOUN ajst-5438 36 30 and and CCONJ ajst-5438 36 31 𝑋 𝑋 PROPN ajst-5438 36 32 is be AUX ajst-5438 36 33 regressed regress VERB ajst-5438 36 34 to to PART ajst-5438 36 35 obtain obtain VERB ajst-5438 36 36 𝛽 𝛽 DET ajst-5438 36 37 initial initial ADJ ajst-5438 36 38 estimate estimate NOUN ajst-5438 36 39 of of ADP ajst-5438 36 40 𝛽 𝛽 NOUN ajst-5438 36 41 5 5 NUM ajst-5438 36 42 . . PUNCT ajst-5438 36 43 using use VERB ajst-5438 36 44 local local ADJ ajst-5438 36 45 polynomial polynomial ADJ ajst-5438 36 46 smoothing smoothing NOUN ajst-5438 36 47 estimation estimation NOUN ajst-5438 36 48 , , PUNCT ajst-5438 36 49 the the DET ajst-5438 36 50 initial initial ADJ ajst-5438 36 51 feasible feasible ADJ ajst-5438 36 52 estimator estimator NOUN ajst-5438 36 53 of of ADP ajst-5438 36 54 the the DET ajst-5438 36 55 connection connection NOUN ajst-5438 36 56 function function NOUN ajst-5438 36 57 g g PROPN ajst-5438 36 58 βˆ™ βˆ™ PROPN ajst-5438 36 59 and and CCONJ ajst-5438 36 60 its its PRON ajst-5438 36 61 first first ADJ ajst-5438 36 62 derivative derivative ADJ ajst-5438 36 63 g g NOUN ajst-5438 36 64 βˆ™ βˆ™ PROPN ajst-5438 36 65 is be AUX ajst-5438 36 66 obtained obtain VERB ajst-5438 36 67 g g NOUN ajst-5438 36 68 and and CCONJ ajst-5438 36 69 g g PROPN ajst-5438 36 70 𝑔 𝑔 PROPN ajst-5438 36 71 𝑒 𝑒 PROPN ajst-5438 36 72 𝑔 𝑔 PROPN ajst-5438 36 73 𝑒;πœƒ,𝛽 𝑒;πœƒ,𝛽 PROPN ajst-5438 36 74 π‘Š π‘Š PROPN ajst-5438 36 75 𝑒;𝛽 𝑒;𝛽 NOUN ajst-5438 36 76 π‘Œ π‘Œ PROPN ajst-5438 36 77 𝑍 𝑍 PROPN ajst-5438 36 78 πœƒ πœƒ NUM ajst-5438 36 79 𝑔 𝑔 NOUN ajst-5438 36 80 𝑒 𝑒 PRON ajst-5438 36 81 𝑔 𝑔 PROPN ajst-5438 36 82 𝑒;πœƒ,𝛽 𝑒;πœƒ,𝛽 PROPN ajst-5438 36 83 π‘Š π‘Š PROPN ajst-5438 36 84 𝑒;𝛽 𝑒;𝛽 NOUN ajst-5438 36 85 π‘Œ π‘Œ PROPN ajst-5438 36 86 𝑍 𝑍 PROPN ajst-5438 36 87 πœƒ πœƒ NOUN ajst-5438 36 88 algorithm algorithm NOUN ajst-5438 36 89 for for ADP ajst-5438 36 90 stage stage NOUN ajst-5438 36 91 two two NUM ajst-5438 37 1 : : PUNCT ajst-5438 37 2 6 6 NUM ajst-5438 37 3 . . X ajst-5438 37 4 use use NOUN ajst-5438 37 5 step step NOUN ajst-5438 37 6 4 4 NUM ajst-5438 37 7 to to PART ajst-5438 37 8 get get VERB ajst-5438 37 9 the the DET ajst-5438 37 10 initial initial ADJ ajst-5438 37 11 estimate estimate NOUN ajst-5438 37 12 𝛽 𝛽 NOUN ajst-5438 37 13 , , PUNCT ajst-5438 37 14 obtained obtain VERB ajst-5438 37 15 by by ADP ajst-5438 37 16 solving solve VERB ajst-5438 37 17 the the DET ajst-5438 37 18 deviation deviation NOUN ajst-5438 37 19 correction correction NOUN ajst-5438 37 20 generalized generalize VERB ajst-5438 37 21 estimation estimation NOUN ajst-5438 37 22 equation equation NOUN ajst-5438 37 23 πœƒ πœƒ NUM ajst-5438 37 24 initial initial ADJ ajst-5438 37 25 estimate estimate NOUN ajst-5438 37 26 of of ADP ajst-5438 37 27 πœƒ πœƒ PRON ajst-5438 37 28 1 1 NUM ajst-5438 37 29 𝑛 𝑛 DET ajst-5438 37 30 π‘Œ π‘Œ PROPN ajst-5438 37 31 𝑍 𝑍 VERB ajst-5438 37 32 πœƒ πœƒ NOUN ajst-5438 37 33 𝑔 𝑔 NOUN ajst-5438 37 34 𝑋 𝑋 PROPN ajst-5438 37 35 𝛽 𝛽 PROPN ajst-5438 37 36 𝑍 𝑍 PROPN ajst-5438 37 37 𝐸 𝐸 NOUN ajst-5438 37 38 𝑍 𝑍 VERB ajst-5438 37 39 𝑋 𝑋 NOUN ajst-5438 37 40 𝛽 𝛽 NOUN ajst-5438 37 41 0 0 NUM ajst-5438 37 42 7 7 NUM ajst-5438 37 43 . . PUNCT ajst-5438 38 1 use use VERB ajst-5438 38 2 the the DET ajst-5438 38 3 updated update VERB ajst-5438 38 4 πœƒ πœƒ NUM ajst-5438 38 5 initial initial ADJ ajst-5438 38 6 estimate estimate NOUN ajst-5438 38 7 of of ADP ajst-5438 38 8 πœƒ πœƒ PRON ajst-5438 38 9 form form VERB ajst-5438 38 10 a a DET ajst-5438 38 11 new new ADJ ajst-5438 38 12 residual residual ADJ ajst-5438 38 13 π‘Œ π‘Œ PROPN ajst-5438 38 14 𝑍 𝑍 PROPN ajst-5438 38 15 πœƒ πœƒ NOUN ajst-5438 38 16 , , PUNCT ajst-5438 38 17 then then ADV ajst-5438 38 18 it it PRON ajst-5438 38 19 is be AUX ajst-5438 38 20 obtained obtain VERB ajst-5438 38 21 by by ADP ajst-5438 38 22 solving solve VERB ajst-5438 38 23 the the DET ajst-5438 38 24 deviation deviation NOUN ajst-5438 38 25 correction correction NOUN ajst-5438 38 26 generalized generalize VERB ajst-5438 38 27 estimation estimation NOUN ajst-5438 38 28 equation equation NOUN ajst-5438 38 29 as as SCONJ ajst-5438 38 30 follows follow VERB ajst-5438 38 31 𝛽 𝛽 PRON ajst-5438 38 32 initial initial ADJ ajst-5438 38 33 estimate estimate NOUN ajst-5438 38 34 of of ADP ajst-5438 38 35 𝛽 𝛽 NOUN ajst-5438 38 36 1 1 NUM ajst-5438 38 37 𝑛 𝑛 DET ajst-5438 38 38 π‘Œ π‘Œ PROPN ajst-5438 38 39 𝑍 𝑍 VERB ajst-5438 38 40 πœƒ πœƒ NOUN ajst-5438 38 41 𝑔 𝑔 NOUN ajst-5438 38 42 𝑋 𝑋 PROPN ajst-5438 38 43 𝛽 𝛽 PROPN ajst-5438 38 44 𝑔 𝑔 PROPN ajst-5438 38 45 𝑋 𝑋 PROPN ajst-5438 38 46 𝛽 𝛽 PROPN ajst-5438 38 47 𝑋 𝑋 PROPN ajst-5438 38 48 𝐸 𝐸 PROPN ajst-5438 38 49 𝑋 𝑋 NOUN ajst-5438 38 50 𝑋 𝑋 PROPN ajst-5438 38 51 𝛽 𝛽 PROPN ajst-5438 38 52 0 0 NUM ajst-5438 38 53 8 8 NUM ajst-5438 38 54 . . PUNCT ajst-5438 39 1 use use VERB ajst-5438 39 2 the the DET ajst-5438 39 3 updated update VERB ajst-5438 39 4 estimates estimate NOUN ajst-5438 39 5 of of ADP ajst-5438 39 6 πœƒ πœƒ NOUN ajst-5438 39 7 and and CCONJ ajst-5438 39 8 𝛽 𝛽 NOUN ajst-5438 39 9 in in ADP ajst-5438 39 10 steps step NOUN ajst-5438 39 11 6 6 NUM ajst-5438 39 12 and and CCONJ ajst-5438 39 13 7 7 NUM ajst-5438 39 14 to to PART ajst-5438 39 15 updated update VERB ajst-5438 39 16 the the DET ajst-5438 39 17 estimate estimate NOUN ajst-5438 39 18 of of ADP ajst-5438 39 19 g g NOUN ajst-5438 39 20 and and CCONJ ajst-5438 39 21 g g PROPN ajst-5438 39 22 , , PUNCT ajst-5438 39 23 following follow VERB ajst-5438 39 24 the the DET ajst-5438 39 25 steps step NOUN ajst-5438 39 26 as as SCONJ ajst-5438 39 27 described describe VERB ajst-5438 39 28 in in ADP ajst-5438 39 29 step step NOUN ajst-5438 39 30 5 5 NUM ajst-5438 39 31 . . PUNCT ajst-5438 40 1 the the DET ajst-5438 40 2 first first ADJ ajst-5438 40 3 stage stage NOUN ajst-5438 40 4 is be AUX ajst-5438 40 5 to to PART ajst-5438 40 6 use use VERB ajst-5438 40 7 the the DET ajst-5438 40 8 linear linear ADJ ajst-5438 40 9 regression regression NOUN ajst-5438 40 10 method method NOUN ajst-5438 40 11 and and CCONJ ajst-5438 40 12 local local ADJ ajst-5438 40 13 linear linear ADJ ajst-5438 40 14 smoothing smooth VERB ajst-5438 40 15 estimation estimation NOUN ajst-5438 40 16 to to PART ajst-5438 40 17 obtain obtain VERB ajst-5438 40 18 the the DET ajst-5438 40 19 initial initial ADJ ajst-5438 40 20 estimates estimate NOUN ajst-5438 40 21 of of ADP ajst-5438 40 22 unknown unknown ADJ ajst-5438 40 23 parameters parameter NOUN ajst-5438 40 24 , , PUNCT ajst-5438 40 25 connection connection NOUN ajst-5438 40 26 functions function NOUN ajst-5438 40 27 and and CCONJ ajst-5438 40 28 their their PRON ajst-5438 40 29 derivatives derivative NOUN ajst-5438 40 30 and and CCONJ ajst-5438 40 31 residuals residual NOUN ajst-5438 40 32 . . PUNCT ajst-5438 41 1 in in ADP ajst-5438 41 2 the the DET ajst-5438 41 3 second second ADJ ajst-5438 41 4 stage stage NOUN ajst-5438 41 5 , , PUNCT ajst-5438 41 6 the the DET ajst-5438 41 7 final final ADJ ajst-5438 41 8 estimates estimate NOUN ajst-5438 41 9 of of ADP ajst-5438 41 10 unknown unknown ADJ ajst-5438 41 11 parameters parameter NOUN ajst-5438 41 12 and and CCONJ ajst-5438 41 13 connection connection NOUN ajst-5438 41 14 functions function NOUN ajst-5438 41 15 are be AUX ajst-5438 41 16 obtained obtain VERB ajst-5438 41 17 by by ADP ajst-5438 41 18 using use VERB ajst-5438 41 19 the the DET ajst-5438 41 20 deviation deviation NOUN ajst-5438 41 21 correction correction NOUN ajst-5438 41 22 generalized generalize VERB ajst-5438 41 23 estimation estimation NOUN ajst-5438 41 24 equation equation NOUN ajst-5438 41 25 . . PUNCT ajst-5438 42 1 the the DET ajst-5438 42 2 algorithm algorithm NOUN ajst-5438 42 3 can can AUX ajst-5438 42 4 obtain obtain VERB ajst-5438 42 5 the the DET ajst-5438 42 6 asymptotic asymptotic ADJ ajst-5438 42 7 property property NOUN ajst-5438 42 8 of of ADP ajst-5438 42 9 the the DET ajst-5438 42 10 unknown unknown ADJ ajst-5438 42 11 parameter parameter NOUN ajst-5438 42 12 estimator estimator NOUN ajst-5438 42 13 without without ADP ajst-5438 42 14 iteration iteration NOUN ajst-5438 42 15 , , PUNCT ajst-5438 42 16 and and CCONJ ajst-5438 42 17 solve solve VERB ajst-5438 42 18 𝛽 𝛽 NOUN ajst-5438 42 19 and and CCONJ ajst-5438 42 20 πœƒ πœƒ PRON ajst-5438 42 21 may may AUX ajst-5438 42 22 be be AUX ajst-5438 42 23 a a DET ajst-5438 42 24 related related ADJ ajst-5438 42 25 problem problem NOUN ajst-5438 42 26 that that PRON ajst-5438 42 27 leads lead VERB ajst-5438 42 28 to to ADP ajst-5438 42 29 inaccurate inaccurate ADJ ajst-5438 42 30 parameter parameter NOUN ajst-5438 42 31 estimation estimation NOUN ajst-5438 42 32 ; ; PUNCT ajst-5438 42 33 in in ADP ajst-5438 42 34 addition addition NOUN ajst-5438 42 35 , , PUNCT ajst-5438 42 36 the the DET ajst-5438 42 37 estimators estimator NOUN ajst-5438 42 38 of of ADP ajst-5438 42 39 the the DET ajst-5438 42 40 connection connection NOUN ajst-5438 42 41 function function NOUN ajst-5438 42 42 g g PROPN ajst-5438 42 43 βˆ™ βˆ™ PROPN ajst-5438 42 44 and and CCONJ ajst-5438 42 45 its its PRON ajst-5438 42 46 derivative derivative ADJ ajst-5438 42 47 g g NOUN ajst-5438 42 48 βˆ™ βˆ™ PROPN ajst-5438 42 49 are be AUX ajst-5438 42 50 also also ADV ajst-5438 42 51 obtained obtain VERB ajst-5438 42 52 . . PUNCT ajst-5438 43 1 2 2 X ajst-5438 43 2 . . X ajst-5438 43 3 main main ADJ ajst-5438 43 4 result result NOUN ajst-5438 43 5 in in ADP ajst-5438 43 6 order order NOUN ajst-5438 43 7 to to PART ajst-5438 43 8 study study VERB ajst-5438 43 9 the the DET ajst-5438 43 10 theoretical theoretical ADJ ajst-5438 43 11 results result NOUN ajst-5438 43 12 of of ADP ajst-5438 43 13 the the DET ajst-5438 43 14 estimators estimator NOUN ajst-5438 43 15 obtained obtain VERB ajst-5438 43 16 by by ADP ajst-5438 43 17 the the DET ajst-5438 43 18 " " PUNCT ajst-5438 43 19 two two NUM ajst-5438 43 20 - - PUNCT ajst-5438 43 21 stage stage NOUN ajst-5438 43 22 estimation estimation NOUN ajst-5438 43 23 method method NOUN ajst-5438 43 24 " " PUNCT ajst-5438 43 25 , , PUNCT ajst-5438 43 26 the the DET ajst-5438 43 27 following follow VERB ajst-5438 43 28 regularity regularity NOUN ajst-5438 43 29 assumptions assumption NOUN ajst-5438 43 30 are be AUX ajst-5438 43 31 first first ADV ajst-5438 43 32 given give VERB ajst-5438 43 33 : : PUNCT ajst-5438 43 34 c1 c1 PROPN ajst-5438 43 35 individuals individual NOUN ajst-5438 43 36 and and CCONJ ajst-5438 43 37 individuals individual NOUN ajst-5438 43 38 are be AUX ajst-5438 43 39 independent independent ADJ ajst-5438 43 40 and and CCONJ ajst-5438 43 41 equally equally ADV ajst-5438 43 42 distributed distribute VERB ajst-5438 43 43 . . PUNCT ajst-5438 44 1 c2 c2 PROPN ajst-5438 44 2 ( ( PUNCT ajst-5438 44 3 i i NOUN ajst-5438 44 4 ) ) PUNCT ajst-5438 44 5 the the DET ajst-5438 44 6 distribution distribution NOUN ajst-5438 44 7 of of ADP ajst-5438 44 8 𝑋 𝑋 PROPN ajst-5438 44 9 has have VERB ajst-5438 44 10 a a DET ajst-5438 44 11 compact compact ADJ ajst-5438 44 12 support support NOUN ajst-5438 44 13 set set VERB ajst-5438 44 14 π’œ π’œ NOUN ajst-5438 44 15 ; ; PUNCT ajst-5438 44 16 ( ( PUNCT ajst-5438 44 17 ii ii NOUN ajst-5438 44 18 ) ) PUNCT ajst-5438 44 19 the the DET ajst-5438 44 20 bounded bounded ADJ ajst-5438 44 21 positive positive ADJ ajst-5438 44 22 function function NOUN ajst-5438 44 23 𝑓 𝑓 PROPN ajst-5438 44 24 𝑑 𝑑 PROPN ajst-5438 44 25 is be AUX ajst-5438 44 26 𝑋 𝑋 PROPN ajst-5438 44 27 𝛽 𝛽 PROPN ajst-5438 44 28 density density NOUN ajst-5438 44 29 function function NOUN ajst-5438 44 30 on on ADP ajst-5438 44 31 𝑇 𝑇 PROPN ajst-5438 44 32 , , PUNCT ajst-5438 44 33 and and CCONJ ajst-5438 44 34 𝛽 𝛽 ADP ajst-5438 44 35 the the DET ajst-5438 44 36 domain domain NOUN ajst-5438 44 37 of of ADP ajst-5438 44 38 satisfies satisfie NOUN ajst-5438 44 39 the the DET ajst-5438 44 40 lipschitz lipschitz NOUN ajst-5438 44 41 condition condition NOUN ajst-5438 44 42 of of ADP ajst-5438 44 43 order order NOUN ajst-5438 45 1 1.here 1.here NUM ajst-5438 45 2 𝑇 𝑇 PROPN ajst-5438 45 3 𝑑 𝑑 ADP ajst-5438 45 4 𝑋 𝑋 PROPN ajst-5438 45 5 𝛽;𝑋 𝛽;𝑋 NOUN ajst-5438 45 6 ∈ ∈ PROPN ajst-5438 45 7 𝐴,𝑖 𝐴,𝑖 NOUN ajst-5438 45 8 1 1 NUM ajst-5438 45 9 , , PUNCT ajst-5438 45 10 β‹― β‹― NOUN ajst-5438 45 11 , , PUNCT ajst-5438 45 12 𝑛,𝑗 𝑛,𝑗 ADJ ajst-5438 45 13 1 1 NUM ajst-5438 45 14 , , PUNCT ajst-5438 45 15 β‹― β‹― PROPN ajst-5438 45 16 , , PUNCT ajst-5438 45 17 π‘š π‘š PROPN ajst-5438 45 18 . . PUNCT ajst-5438 46 1 c3 c3 PROPN ajst-5438 46 2 ( ( PUNCT ajst-5438 46 3 i i NOUN ajst-5438 46 4 ) ) PUNCT ajst-5438 46 5 join join VERB ajst-5438 46 6 functions function NOUN ajst-5438 46 7 g g PROPN ajst-5438 46 8 and and CCONJ ajst-5438 46 9 g g PROPN ajst-5438 46 10 has have VERB ajst-5438 46 11 a a DET ajst-5438 46 12 second second ADJ ajst-5438 46 13 order order NOUN ajst-5438 46 14 continuous continuous ADJ ajst-5438 46 15 partial partial ADJ ajst-5438 46 16 derivative derivative NOUN ajst-5438 46 17 , , PUNCT ajst-5438 46 18 whereg whereg NOUN ajst-5438 46 19 is be AUX ajst-5438 46 20 the the DET ajst-5438 46 21 function function NOUN ajst-5438 46 22 vector vector NOUN ajst-5438 46 23 g g PROPN ajst-5438 46 24 the the DET ajst-5438 46 25 ith ith PROPN ajst-5438 46 26 component component NOUN ajst-5438 46 27 of of ADP ajst-5438 46 28 𝑖 𝑖 PRON ajst-5438 46 29 , , PUNCT ajst-5438 46 30 1 1 NUM ajst-5438 46 31 𝑖 𝑖 PRON ajst-5438 46 32 π‘ž,g1 π‘ž,g1 NOUN ajst-5438 46 33 𝑑 𝑑 PROPN ajst-5438 46 34 𝐸 𝐸 ADJ ajst-5438 46 35 𝑍𝑖𝑗 𝑍𝑖𝑗 PROPN ajst-5438 46 36 𝑋𝑖𝑗 𝑋𝑖𝑗 PROPN ajst-5438 46 37 𝑇 𝑇 PROPN ajst-5438 46 38 𝛽 𝛽 PROPN ajst-5438 46 39 𝑑 𝑑 PROPN ajst-5438 46 40 ; ; PUNCT ajst-5438 46 41 ( ( PUNCT ajst-5438 46 42 ii ii NOUN ajst-5438 46 43 ) ) PUNCT ajst-5438 46 44 g g NOUN ajst-5438 46 45 satisfies satisfy VERB ajst-5438 46 46 the the DET ajst-5438 46 47 first first ADJ ajst-5438 46 48 - - PUNCT ajst-5438 46 49 order order NOUN ajst-5438 46 50 lipschitz lipschitz NOUN ajst-5438 46 51 condition condition NOUN ajst-5438 46 52 , , PUNCT ajst-5438 46 53 where where SCONJ ajst-5438 46 54 g g PROPN ajst-5438 46 55 is be AUX ajst-5438 46 56 the the DET ajst-5438 46 57 jth jth PROPN ajst-5438 46 58 component component NOUN ajst-5438 46 59 of of ADP ajst-5438 46 60 g g PROPN ajst-5438 46 61 , , PUNCT ajst-5438 46 62 1 1 NUM ajst-5438 46 63 𝑗 𝑗 PROPN ajst-5438 46 64 𝑝,𝑔 𝑝,𝑔 X ajst-5438 46 65 𝑑 𝑑 NOUN ajst-5438 46 66 𝐸 𝐸 ADJ ajst-5438 46 67 𝑋 𝑋 PROPN ajst-5438 46 68 𝑋 𝑋 PROPN ajst-5438 46 69 𝛽 𝛽 PROPN ajst-5438 46 70 𝑑 𝑑 PROPN ajst-5438 46 71 . . PUNCT ajst-5438 47 1 c4 c4 NOUN ajst-5438 47 2 on on ADP ajst-5438 47 3 𝑅 𝑅 PROPN ajst-5438 47 4 , , PUNCT ajst-5438 47 5 the the DET ajst-5438 47 6 kernel kernel NOUN ajst-5438 47 7 function function NOUN ajst-5438 47 8 𝐾 𝐾 PROPN ajst-5438 47 9 βˆ™ βˆ™ PROPN ajst-5438 47 10 is be AUX ajst-5438 47 11 a a DET ajst-5438 47 12 continuous continuous ADJ ajst-5438 47 13 bounded bound VERB ajst-5438 47 14 probability probability NOUN ajst-5438 47 15 density density NOUN ajst-5438 47 16 function function NOUN ajst-5438 47 17 that that PRON ajst-5438 47 18 satisfies satisfy VERB ajst-5438 47 19 the the DET ajst-5438 47 20 lipschitz lipschitz NOUN ajst-5438 47 21 condition condition NOUN ajst-5438 47 22 and and CCONJ ajst-5438 47 23 satisfies satisfy VERB ajst-5438 47 24 𝑒 𝑒 X ajst-5438 47 25 𝐾 𝐾 PROPN ajst-5438 47 26 𝑒 𝑒 X ajst-5438 47 27 𝑑𝑒 𝑑𝑒 PROPN ajst-5438 47 28 0 0 NUM ajst-5438 47 29 , , PUNCT ajst-5438 47 30 |𝑒| |𝑒| PROPN ajst-5438 47 31 𝐾 𝐾 PROPN ajst-5438 47 32 𝑒 𝑒 PROPN ajst-5438 47 33 𝑑𝑒 𝑑𝑒 PROPN ajst-5438 47 34 ∞. ∞. PROPN ajst-5438 47 35 c5 c5 PROPN ajst-5438 47 36 ( ( PUNCT ajst-5438 47 37 i i PROPN ajst-5438 47 38 ) ) PUNCT ajst-5438 47 39 it it PRON ajst-5438 47 40 has have VERB ajst-5438 47 41 a a DET ajst-5438 47 42 constant constant ADJ ajst-5438 47 43 𝑀 𝑀 NOUN ajst-5438 47 44 0 0 NUM ajst-5438 47 45 , , PUNCT ajst-5438 47 46 so so SCONJ ajst-5438 47 47 that that SCONJ ajst-5438 47 48 for for ADP ajst-5438 47 49 any𝑖,𝑗 any𝑖,𝑗 NOUN ajst-5438 47 50 satisfies satisfie NOUN ajst-5438 47 51 sup sup NOUN ajst-5438 47 52 ∈ ∈ PROPN ajst-5438 47 53 𝐸 𝐸 PROPN ajst-5438 47 54 𝑍 𝑍 VERB ajst-5438 47 55 𝑋 𝑋 PROPN ajst-5438 47 56 𝛽 𝛽 PROPN ajst-5438 47 57 𝑑 𝑑 PROPN ajst-5438 47 58 𝑀 𝑀 PROPN ajst-5438 47 59 ∞ ∞ PROPN ajst-5438 47 60 ; ; PUNCT ajst-5438 47 61 ( ( PUNCT ajst-5438 47 62 ii ii NOUN ajst-5438 47 63 ) ) PUNCT ajst-5438 47 64 random random ADJ ajst-5438 47 65 error error NOUN ajst-5438 47 66 πœ€ πœ€ NOUN ajst-5438 47 67 independent independent ADJ ajst-5438 47 68 of of ADP ajst-5438 47 69 covariate covariate ADJ ajst-5438 47 70 𝑋 𝑋 NOUN ajst-5438 47 71 and and CCONJ ajst-5438 47 72 𝑍 𝑍 PROPN ajst-5438 47 73 , , PUNCT ajst-5438 47 74 and and CCONJ ajst-5438 47 75 there there PRON ajst-5438 47 76 is be VERB ajst-5438 47 77 a a DET ajst-5438 47 78 constant constant ADJ ajst-5438 47 79 𝑀 𝑀 NOUN ajst-5438 47 80 0 0 NUM ajst-5438 47 81 , , PUNCT ajst-5438 47 82 πœ€ πœ€ VERB ajst-5438 47 83 0,0 0,0 NUM ajst-5438 47 84 π‘£π‘Žπ‘Ÿ π‘£π‘Žπ‘Ÿ NOUN ajst-5438 47 85 πœ€ πœ€ PROPN ajst-5438 47 86 𝜎 𝜎 PROPN ajst-5438 47 87 ∞,𝐸 ∞,𝐸 NOUN ajst-5438 47 88 πœ€ πœ€ PROPN ajst-5438 47 89 𝑀 𝑀 PROPN ajst-5438 47 90 ∞. ∞. PROPN ajst-5438 47 91 c6 c6 PROPN ajst-5438 47 92 when when SCONJ ajst-5438 47 93 𝑛 𝑛 ADJ ajst-5438 47 94 β†’ β†’ PUNCT ajst-5438 47 95 ∞,bandwidth ∞,bandwidth ADJ ajst-5438 47 96 sequence sequence NOUN ajst-5438 47 97 β„Ž β„Ž NOUN ajst-5438 47 98 and and CCONJ ajst-5438 47 99 β„Ž β„Ž ADP ajst-5438 47 100 satisfie satisfie NOUN ajst-5438 47 101 ( ( PUNCT ajst-5438 47 102 i i NOUN ajst-5438 47 103 ) ) PUNCT ajst-5438 47 104 π‘›β„Ž π‘›β„Ž NOUN ajst-5438 47 105 /log /log PUNCT ajst-5438 47 106 𝑛 𝑛 PROPN ajst-5438 47 107 β†’ β†’ SYM ajst-5438 47 108 ∞ ∞ PROPN ajst-5438 47 109 , , PUNCT ajst-5438 47 110 lim lim PROPN ajst-5438 47 111 β†’ β†’ SYM ajst-5438 47 112 π‘›β„Ž π‘›β„Ž PROPN ajst-5438 47 113 ∞ ∞ PROPN ajst-5438 47 114 ; ; PUNCT ajst-5438 47 115 ( ( PUNCT ajst-5438 47 116 ii ii NOUN ajst-5438 47 117 ) ) PUNCT ajst-5438 47 118 π‘›β„Ž π‘›β„Ž VERB ajst-5438 47 119 β„Ž β„Ž PROPN ajst-5438 47 120 /log /log PUNCT ajst-5438 47 121 𝑛 𝑛 PROPN ajst-5438 47 122 β†’ β†’ SYM ajst-5438 47 123 ∞,π‘›β„Ž ∞,π‘›β„Ž NUM ajst-5438 47 124 β†’ β†’ SYM ajst-5438 47 125 ∞. ∞. PROPN ajst-5438 47 126 c7 c7 PROPN ajst-5438 47 127 definition definition NOUN ajst-5438 47 128 π‘Œβˆ— π‘Œβˆ— NOUN ajst-5438 48 1 π‘Œπ‘–π‘— π‘Œπ‘–π‘— PROPN ajst-5438 48 2 βˆ— βˆ— VERB ajst-5438 48 3 𝑍𝑖𝑗 𝑍𝑖𝑗 PROPN ajst-5438 48 4 𝑇 𝑇 PROPN ajst-5438 48 5 πœƒ0οΌŒπ›΄ πœƒ0οΌŒπ›΄ NOUN ajst-5438 48 6 is be AUX ajst-5438 48 7 a a DET ajst-5438 48 8 bounded bounded ADJ ajst-5438 48 9 positive positive ADJ ajst-5438 48 10 definite definite ADJ ajst-5438 48 11 matrix matrix NOUN ajst-5438 48 12 𝛴 𝛴 NOUN ajst-5438 48 13 πΆπ‘œπ‘£ πΆπ‘œπ‘£ NOUN ajst-5438 48 14 𝑍 𝑍 NOUN ajst-5438 48 15 𝐸 𝐸 NOUN ajst-5438 48 16 𝑍|𝑋 𝑍|𝑋 NOUN ajst-5438 48 17 𝛽 𝛽 NOUN ajst-5438 48 18 𝐡 𝐡 NOUN ajst-5438 48 19 𝐸 𝐸 PROPN ajst-5438 48 20 𝑔 𝑔 PROPN ajst-5438 48 21 𝑋 𝑋 PROPN ajst-5438 48 22 𝛽 𝛽 PROPN ajst-5438 48 23 𝑋 𝑋 PROPN ajst-5438 48 24 𝑋|𝑋 𝑋|𝑋 PUNCT ajst-5438 48 25 𝛽 𝛽 NOUN ajst-5438 48 26 𝑋 𝑋 PROPN ajst-5438 48 27 𝑋|𝑋 𝑋|𝑋 PROPN ajst-5438 48 28 𝛽 𝛽 PROPN ajst-5438 48 29 𝐡 𝐡 NOUN ajst-5438 48 30 𝐸 𝐸 PROPN ajst-5438 48 31 𝑓 𝑓 DET ajst-5438 48 32 βˆ—π‘” βˆ—π‘” NOUN ajst-5438 48 33 𝑋 𝑋 PROPN ajst-5438 48 34 𝛽 𝛽 PROPN ajst-5438 48 35 𝑔 𝑔 PROPN ajst-5438 48 36 𝑋 𝑋 PROPN ajst-5438 48 37 𝛽 𝛽 PROPN ajst-5438 48 38 𝑋 𝑋 PROPN ajst-5438 48 39 𝑋|𝑋 𝑋|𝑋 PUNCT ajst-5438 48 40 𝛽 𝛽 NOUN ajst-5438 48 41 𝑋 𝑋 PROPN ajst-5438 48 42 𝑋|𝑋 𝑋|𝑋 PROPN ajst-5438 48 43 𝛽 𝛽 NOUN ajst-5438 48 44 condition condition NOUN ajst-5438 48 45 ( ( PUNCT ajst-5438 48 46 c1 c1 NOUN ajst-5438 48 47 ) ) PUNCT ajst-5438 48 48 is be AUX ajst-5438 48 49 the the DET ajst-5438 48 50 assumption assumption NOUN ajst-5438 48 51 of of ADP ajst-5438 48 52 independence independence NOUN ajst-5438 48 53 . . PUNCT ajst-5438 49 1 see see VERB ajst-5438 49 2 reference reference NOUN ajst-5438 49 3 [ [ X ajst-5438 49 4 11 11 NUM ajst-5438 49 5 ] ] PUNCT ajst-5438 49 6 for for ADP ajst-5438 49 7 details detail NOUN ajst-5438 49 8 . . PUNCT ajst-5438 50 1 lipschitz lipschitz NOUN ajst-5438 50 2 condition condition NOUN ajst-5438 50 3 and and CCONJ ajst-5438 50 4 standard standard ADJ ajst-5438 50 5 smoothness smoothness ADJ ajst-5438 50 6 condition condition NOUN ajst-5438 50 7 in in ADP ajst-5438 50 8 condition condition NOUN ajst-5438 50 9 ( ( PUNCT ajst-5438 50 10 c2 c2 PROPN ajst-5438 50 11 ) ) PUNCT ajst-5438 50 12 and and CCONJ ajst-5438 50 13 condition condition NOUN ajst-5438 50 14 ( ( PUNCT ajst-5438 50 15 3 3 NUM ajst-5438 50 16 ) ) PUNCT ajst-5438 50 17 . . PUNCT ajst-5438 51 1 for for ADP ajst-5438 51 2 some some DET ajst-5438 51 3 common common ADJ ajst-5438 51 4 regularity regularity NOUN ajst-5438 51 5 and and CCONJ ajst-5438 51 6 slip slip NOUN ajst-5438 51 7 assumptions assumption NOUN ajst-5438 51 8 of of ADP ajst-5438 51 9 conditional conditional ADJ ajst-5438 51 10 ( ( PUNCT ajst-5438 51 11 c4 c4 NOUN ajst-5438 51 12 ) ) PUNCT ajst-5438 51 13 kernel kernel NOUN ajst-5438 51 14 functions function NOUN ajst-5438 51 15 , , PUNCT ajst-5438 51 16 to to PART ajst-5438 51 17 ensure ensure VERB ajst-5438 51 18 that that SCONJ ajst-5438 51 19 the the DET ajst-5438 51 20 theoretical theoretical ADJ ajst-5438 51 21 results result NOUN ajst-5438 51 22 are be AUX ajst-5438 51 23 well well ADV ajst-5438 51 24 established establish VERB ajst-5438 51 25 . . PUNCT ajst-5438 52 1 the the DET ajst-5438 52 2 condition condition NOUN ajst-5438 52 3 ( ( PUNCT ajst-5438 52 4 c5 c5 PROPN ajst-5438 52 5 ) ) PUNCT ajst-5438 52 6 is be AUX ajst-5438 52 7 to to PART ajst-5438 52 8 satisfy satisfy VERB ajst-5438 52 9 the the DET ajst-5438 52 10 existence existence NOUN ajst-5438 52 11 of of ADP ajst-5438 52 12 the the DET ajst-5438 52 13 second second ADJ ajst-5438 52 14 moment moment NOUN ajst-5438 52 15 , , PUNCT ajst-5438 52 16 so so SCONJ ajst-5438 52 17 that that SCONJ ajst-5438 52 18 the the DET ajst-5438 52 19 proposed propose VERB ajst-5438 52 20 parameter parameter NOUN ajst-5438 52 21 and and CCONJ ajst-5438 52 22 the the DET ajst-5438 52 23 single single ADJ ajst-5438 52 24 exponential exponential ADJ ajst-5438 52 25 function function NOUN ajst-5438 52 26 estimator estimator NOUN ajst-5438 52 27 are be AUX ajst-5438 52 28 consistent consistent ADJ ajst-5438 52 29 and and CCONJ ajst-5438 52 30 asymptotically asymptotically ADV ajst-5438 52 31 normal normal ADJ ajst-5438 52 32 . . PUNCT ajst-5438 53 1 condition condition NOUN ajst-5438 53 2 ( ( PUNCT ajst-5438 53 3 c6 c6 PROPN ajst-5438 53 4 ) ) PUNCT ajst-5438 53 5 is be AUX ajst-5438 53 6 the the DET ajst-5438 53 7 bandwidth bandwidth ADJ ajst-5438 53 8 h h NOUN ajst-5438 53 9 used use VERB ajst-5438 53 10 to to PART ajst-5438 53 11 estimate estimate VERB ajst-5438 53 12 the the DET ajst-5438 53 13 connection connection NOUN ajst-5438 53 14 function function VERB ajst-5438 53 15 g g PROPN ajst-5438 53 16 βˆ™ βˆ™ PROPN ajst-5438 53 17 , , PUNCT ajst-5438 53 18 and and CCONJ ajst-5438 53 19 the the DET ajst-5438 53 20 other other ADJ ajst-5438 53 21 band band NOUN ajst-5438 53 22 width width NOUN ajst-5438 53 23 β„Ž β„Ž PROPN ajst-5438 53 24 is be AUX ajst-5438 53 25 to to PART ajst-5438 53 26 control control VERB ajst-5438 53 27 the the DET ajst-5438 53 28 change change NOUN ajst-5438 53 29 of of ADP ajst-5438 53 30 g g PROPN ajst-5438 53 31 βˆ™ βˆ™ PROPN ajst-5438 53 32 , , PUNCT ajst-5438 53 33 see see VERB ajst-5438 53 34 reference reference NOUN ajst-5438 53 35 [ [ X ajst-5438 53 36 12 12 NUM ajst-5438 53 37 ] ] PUNCT ajst-5438 53 38 . . PUNCT ajst-5438 54 1 the the DET ajst-5438 54 2 condition condition NOUN ajst-5438 54 3 ( ( PUNCT ajst-5438 54 4 c7 c7 PROPN ajst-5438 54 5 ) ) PUNCT ajst-5438 54 6 ensures ensure VERB ajst-5438 54 7 that that SCONJ ajst-5438 54 8 the the DET ajst-5438 54 9 variance variance NOUN ajst-5438 54 10 limit limit NOUN ajst-5438 54 11 of of ADP ajst-5438 54 12 the the DET ajst-5438 54 13 parameter parameter NOUN ajst-5438 54 14 estimator estimator NOUN ajst-5438 54 15 exists exist VERB ajst-5438 54 16 . . PUNCT ajst-5438 55 1 let let VERB ajst-5438 55 2 𝜌 𝜌 PRON ajst-5438 55 3 𝑒 𝑒 ADP ajst-5438 55 4 𝐾 𝐾 PROPN ajst-5438 55 5 𝑒 𝑒 X ajst-5438 55 6 𝑑𝑒 𝑑𝑒 PROPN ajst-5438 55 7 , , PUNCT ajst-5438 55 8 𝜚 𝜚 NOUN ajst-5438 55 9 𝐾 𝐾 NOUN ajst-5438 55 10 𝑒 𝑒 X ajst-5438 55 11 𝑑𝑒 𝑑𝑒 PROPN ajst-5438 55 12 , , PUNCT ajst-5438 55 13 𝑙 𝑙 PROPN ajst-5438 55 14 1,2,3 1,2,3 NUM ajst-5438 55 15 ， ， NOUN ajst-5438 55 16 the the DET ajst-5438 55 17 following following NOUN ajst-5438 55 18 are be AUX ajst-5438 55 19 the the DET ajst-5438 55 20 connection connection NOUN ajst-5438 55 21 function function NOUN ajst-5438 55 22 g g PROPN ajst-5438 55 23 βˆ™ βˆ™ PROPN ajst-5438 55 24 and and CCONJ ajst-5438 55 25 unknown unknown ADJ ajst-5438 55 26 parameter parameter NOUN ajst-5438 55 27 components component NOUN ajst-5438 55 28 πœƒ πœƒ NOUN ajst-5438 55 29 and and CCONJ ajst-5438 55 30 𝛽 𝛽 NOUN ajst-5438 55 31 results result NOUN ajst-5438 55 32 of of ADP ajst-5438 55 33 asymptotic asymptotic ADJ ajst-5438 55 34 114 114 NUM ajst-5438 55 35 properties property NOUN ajst-5438 55 36 of of ADP ajst-5438 55 37 . . PUNCT ajst-5438 56 1 theorem theorem ADJ ajst-5438 56 2 1 1 NUM ajst-5438 56 3 assume assume VERB ajst-5438 56 4 that that SCONJ ajst-5438 56 5 the the DET ajst-5438 56 6 above above ADJ ajst-5438 56 7 regularity regularity NOUN ajst-5438 56 8 and and CCONJ ajst-5438 56 9 smoothness smoothness ADJ ajst-5438 56 10 conditions condition NOUN ajst-5438 56 11 c1 c1 NOUN ajst-5438 56 12 - - PUNCT ajst-5438 56 13 c4 c4 NOUN ajst-5438 56 14 hold hold VERB ajst-5438 56 15 , , PUNCT ajst-5438 56 16 and and CCONJ ajst-5438 56 17 if if SCONJ ajst-5438 56 18 π‘›β„Ž π‘›β„Ž NOUN ajst-5438 56 19 β†’ β†’ SYM ajst-5438 56 20 0 0 NUM ajst-5438 56 21 , , PUNCT ajst-5438 56 22 the the DET ajst-5438 56 23 initial initial ADJ ajst-5438 56 24 estimator𝛽 estimator𝛽 NOUN ajst-5438 56 25 , , PUNCT ajst-5438 56 26 πœƒ πœƒ X ajst-5438 56 27 satisfied satisfied ADJ ajst-5438 56 28 𝛽 𝛽 PRON ajst-5438 56 29 𝛽 𝛽 NOUN ajst-5438 56 30 𝑂 𝑂 NOUN ajst-5438 56 31 𝑛 𝑛 PROPN ajst-5438 56 32 / / SYM ajst-5438 56 33 , , PUNCT ajst-5438 56 34 πœƒ πœƒ X ajst-5438 56 35 πœƒ πœƒ NOUN ajst-5438 56 36 𝑂 𝑂 NOUN ajst-5438 56 37 𝑛 𝑛 PROPN ajst-5438 56 38 / / SYM ajst-5438 56 39 , , PUNCT ajst-5438 56 40 then then ADV ajst-5438 56 41 when when SCONJ ajst-5438 56 42 𝑛 𝑛 PROPN ajst-5438 56 43 β†’ β†’ SYM ajst-5438 56 44 ∞ ∞ PROPN ajst-5438 56 45 βˆšπ‘›β„Ž βˆšπ‘›β„Ž PROPN ajst-5438 56 46 𝑔 𝑔 PROPN ajst-5438 56 47 𝑒;𝛽,πœƒ 𝑒;𝛽,πœƒ PROPN ajst-5438 56 48 𝑔 𝑔 PROPN ajst-5438 56 49 𝑒 𝑒 ADP ajst-5438 56 50 β„Ž β„Ž ADP ajst-5438 56 51 𝑏 𝑏 PROPN ajst-5438 56 52 𝑒 𝑒 NOUN ajst-5438 56 53 β†’ β†’ PUNCT ajst-5438 56 54 𝑁 𝑁 PROPN ajst-5438 56 55 0,𝐴 0,𝐴 NUM ajst-5438 56 56 𝑒 𝑒 NOUN ajst-5438 56 57 here here ADV ajst-5438 56 58 𝑏 𝑏 PROPN ajst-5438 56 59 𝑒 𝑒 PROPN ajst-5438 56 60 𝑔 𝑔 PROPN ajst-5438 56 61 𝑒 𝑒 X ajst-5438 56 62 𝜌 𝜌 X ajst-5438 57 1 ， ， PROPN ajst-5438 57 2 𝐴 𝐴 PROPN ajst-5438 57 3 𝑒 𝑒 PROPN ajst-5438 57 4 βˆ— βˆ— PROPN ajst-5438 57 5 𝑔 𝑔 PROPN ajst-5438 57 6 𝑒 𝑒 PROPN ajst-5438 57 7 𝑒 𝑒 X ajst-5438 57 8 theorem theorem ADJ ajst-5438 57 9 2 2 NUM ajst-5438 57 10 assume assume VERB ajst-5438 57 11 that that SCONJ ajst-5438 57 12 the the DET ajst-5438 57 13 above above ADJ ajst-5438 57 14 regularity regularity NOUN ajst-5438 57 15 and and CCONJ ajst-5438 57 16 smoothness smoothness ADJ ajst-5438 57 17 conditions condition NOUN ajst-5438 57 18 c1 c1 PROPN ajst-5438 57 19 - - PUNCT ajst-5438 57 20 c7 c7 PROPN ajst-5438 57 21 hold hold VERB ajst-5438 57 22 , , PUNCT ajst-5438 57 23 and and CCONJ ajst-5438 57 24 the the DET ajst-5438 57 25 initial initial ADJ ajst-5438 57 26 estimator estimator NOUN ajst-5438 57 27 𝛽 𝛽 PROPN ajst-5438 57 28 , , PUNCT ajst-5438 57 29 𝛽 𝛽 PROPN ajst-5438 57 30 satisfied satisfy VERB ajst-5438 57 31 𝛽 𝛽 PROPN ajst-5438 57 32 𝛽 𝛽 NOUN ajst-5438 57 33 𝑂 𝑂 NOUN ajst-5438 57 34 𝑛 𝑛 PROPN ajst-5438 57 35 / / SYM ajst-5438 57 36 , , PUNCT ajst-5438 57 37 𝛽 𝛽 NOUN ajst-5438 57 38 𝛽 𝛽 NOUN ajst-5438 57 39 𝑂 𝑂 NOUN ajst-5438 57 40 𝑛 𝑛 PROPN ajst-5438 57 41 / / SYM ajst-5438 57 42 , , PUNCT ajst-5438 57 43 then then ADV ajst-5438 57 44 when when SCONJ ajst-5438 57 45 𝑛 𝑛 PROPN ajst-5438 57 46 β†’ β†’ SYM ajst-5438 57 47 ∞ ∞ PROPN ajst-5438 57 48 βˆšπ‘› βˆšπ‘› ADP ajst-5438 57 49 πœƒ πœƒ NOUN ajst-5438 57 50 πœƒ πœƒ X ajst-5438 57 51 β†’ β†’ PUNCT ajst-5438 57 52 𝑁 𝑁 ADJ ajst-5438 57 53 0,𝜎 0,𝜎 NUM ajst-5438 57 54 𝛴 𝛴 NOUN ajst-5438 57 55 βˆšπ‘› βˆšπ‘› ADP ajst-5438 57 56 𝛽 𝛽 NOUN ajst-5438 57 57 𝛽 𝛽 NOUN ajst-5438 57 58 β†’ β†’ SYM ajst-5438 57 59 𝑁 𝑁 PROPN ajst-5438 57 60 0,𝜎 0,𝜎 NUM ajst-5438 57 61 𝐡 𝐡 NOUN ajst-5438 57 62 𝐡 𝐡 NOUN ajst-5438 57 63 𝐡 𝐡 PROPN ajst-5438 57 64 where where SCONJ ajst-5438 57 65 𝐡 𝐡 NOUN ajst-5438 57 66 is be AUX ajst-5438 57 67 the the DET ajst-5438 57 68 inverse inverse NOUN ajst-5438 57 69 of of ADP ajst-5438 57 70 𝐡 𝐡 NOUN ajst-5438 57 71 , , PUNCT ajst-5438 57 72 the the DET ajst-5438 57 73 definition definition NOUN ajst-5438 57 74 of of ADP ajst-5438 57 75 𝛴、𝐡 𝛴、𝐡 PRON ajst-5438 57 76 and and CCONJ ajst-5438 57 77 𝐡 𝐡 PRON ajst-5438 57 78 see see VERB ajst-5438 57 79 c7 c7 PROPN ajst-5438 57 80 . . PUNCT ajst-5438 58 1 3 3 X ajst-5438 58 2 . . X ajst-5438 58 3 simulation simulation NOUN ajst-5438 58 4 study study NOUN ajst-5438 58 5 in in ADP ajst-5438 58 6 this this DET ajst-5438 58 7 section section NOUN ajst-5438 58 8 , , PUNCT ajst-5438 58 9 this this DET ajst-5438 58 10 paper paper NOUN ajst-5438 58 11 considers consider VERB ajst-5438 58 12 the the DET ajst-5438 58 13 effectiveness effectiveness NOUN ajst-5438 58 14 of of ADP ajst-5438 58 15 the the DET ajst-5438 58 16 " " PUNCT ajst-5438 58 17 two two NUM ajst-5438 58 18 - - PUNCT ajst-5438 58 19 stage stage NOUN ajst-5438 58 20 estimation estimation NOUN ajst-5438 58 21 method method NOUN ajst-5438 58 22 " " PUNCT ajst-5438 58 23 by by ADP ajst-5438 58 24 applying apply VERB ajst-5438 58 25 the the DET ajst-5438 58 26 monte monte PROPN ajst-5438 58 27 carlo carlo PROPN ajst-5438 58 28 method method NOUN ajst-5438 58 29 in in ADP ajst-5438 58 30 the the DET ajst-5438 58 31 case case NOUN ajst-5438 58 32 of of ADP ajst-5438 58 33 limited limited ADJ ajst-5438 58 34 samples sample NOUN ajst-5438 58 35 . . PUNCT ajst-5438 59 1 first first ADV ajst-5438 59 2 , , PUNCT ajst-5438 59 3 generate generate VERB ajst-5438 59 4 some some DET ajst-5438 59 5 random random ADJ ajst-5438 59 6 numbers number NOUN ajst-5438 59 7 in in ADP ajst-5438 59 8 the the DET ajst-5438 59 9 following following ADJ ajst-5438 59 10 model model NOUN ajst-5438 59 11 : : PUNCT ajst-5438 59 12 π‘Œ π‘Œ PROPN ajst-5438 59 13 𝑍 𝑍 VERB ajst-5438 59 14 πœƒ πœƒ NOUN ajst-5438 59 15 𝑔 𝑔 NOUN ajst-5438 59 16 𝑋 𝑋 PROPN ajst-5438 59 17 𝛽 𝛽 PROPN ajst-5438 59 18 πœ€ πœ€ PROPN ajst-5438 59 19 , , PUNCT ajst-5438 59 20 𝑖 𝑖 PROPN ajst-5438 59 21 1 1 NUM ajst-5438 59 22 , , PUNCT ajst-5438 59 23 β‹― β‹― NOUN ajst-5438 59 24 , , PUNCT ajst-5438 59 25 𝑛,𝑗 𝑛,𝑗 ADJ ajst-5438 59 26 1 1 NUM ajst-5438 59 27 , , PUNCT ajst-5438 59 28 β‹― β‹― PROPN ajst-5438 59 29 , , PUNCT ajst-5438 59 30 π‘š π‘š X ajst-5438 59 31 where where SCONJ ajst-5438 59 32 𝑍 𝑍 PROPN ajst-5438 59 33 is be AUX ajst-5438 59 34 a a DET ajst-5438 59 35 covariate covariate NOUN ajst-5438 59 36 , , PUNCT ajst-5438 59 37 a a DET ajst-5438 59 38 0 0 NUM ajst-5438 59 39 1 1 NUM ajst-5438 59 40 distribution distribution NOUN ajst-5438 59 41 with with ADP ajst-5438 59 42 a a DET ajst-5438 59 43 parameter parameter NOUN ajst-5438 59 44 of of ADP ajst-5438 59 45 0.5 0.5 NUM ajst-5438 59 46 , , PUNCT ajst-5438 59 47 𝑋 𝑋 PROPN ajst-5438 59 48 𝑋 𝑋 PROPN ajst-5438 59 49 , , PUNCT ajst-5438 59 50 𝑋 𝑋 PROPN ajst-5438 59 51 , , PUNCT ajst-5438 59 52 𝑋 𝑋 PROPN ajst-5438 59 53 , , PUNCT ajst-5438 59 54 𝑋 𝑋 NOUN ajst-5438 59 55 , , PUNCT ajst-5438 59 56 𝑋 𝑋 PROPN ajst-5438 59 57 𝑋 𝑋 PROPN ajst-5438 59 58 、 、 NOUN ajst-5438 59 59 𝑋 𝑋 NOUN ajst-5438 59 60 、 、 NOUN ajst-5438 59 61 𝑋 𝑋 NOUN ajst-5438 59 62 、 、 NOUN ajst-5438 59 63 𝑋 𝑋 PROPN ajst-5438 59 64 and and CCONJ ajst-5438 59 65 𝑋 𝑋 PROPN ajst-5438 59 66 are be AUX ajst-5438 59 67 independent independent ADJ ajst-5438 59 68 of of ADP ajst-5438 59 69 each each DET ajst-5438 59 70 other other ADJ ajst-5438 59 71 and and CCONJ ajst-5438 59 72 are be AUX ajst-5438 59 73 uniform uniform ADJ ajst-5438 59 74 distribution distribution NOUN ajst-5438 59 75 from from ADP ajst-5438 59 76 the the DET ajst-5438 59 77 0,1 0,1 NUM ajst-5438 59 78 interval interval NOUN ajst-5438 59 79 . . PUNCT ajst-5438 60 1 during during ADP ajst-5438 60 2 the the DET ajst-5438 60 3 simulation simulation NOUN ajst-5438 60 4 experiment experiment NOUN ajst-5438 60 5 , , PUNCT ajst-5438 60 6 errors error NOUN ajst-5438 60 7 πœ€ πœ€ NOUN ajst-5438 60 8 πœ€ πœ€ PROPN ajst-5438 60 9 , , PUNCT ajst-5438 60 10 πœ€ πœ€ X ajst-5438 60 11 , , PUNCT ajst-5438 60 12 πœ€ πœ€ X ajst-5438 60 13 , , PUNCT ajst-5438 60 14 πœ€ πœ€ X ajst-5438 60 15 , , PUNCT ajst-5438 60 16 πœ€ πœ€ X ajst-5438 60 17 , , PUNCT ajst-5438 60 18 𝑖 𝑖 PROPN ajst-5438 60 19 1,2,3,4,5 1,2,3,4,5 NUM ajst-5438 60 20 obey obey VERB ajst-5438 60 21 standard standard ADJ ajst-5438 60 22 normal normal ADJ ajst-5438 60 23 distribution distribution NOUN ajst-5438 60 24 . . PUNCT ajst-5438 61 1 𝛽 𝛽 NOUN ajst-5438 61 2 0.5,0,0.5,0.5,-0.5 0.5,0,0.5,0.5,-0.5 NUM ajst-5438 61 3 , , PUNCT ajst-5438 61 4 𝛽 𝛽 NOUN ajst-5438 61 5 0.75,0.5,-0.25,-0.25,0.2 0.75,0.5,-0.25,-0.25,0.2 PROPN ajst-5438 61 6 and and CCONJ ajst-5438 61 7 πœƒ πœƒ SYM ajst-5438 61 8 1 1 NUM ajst-5438 61 9 the the DET ajst-5438 61 10 connection connection NOUN ajst-5438 61 11 function function VERB ajst-5438 61 12 𝑔 𝑔 PROPN ajst-5438 61 13 𝑒 𝑒 PROPN ajst-5438 61 14 sin sin NOUN ajst-5438 61 15 ， ， PROPN ajst-5438 61 16 𝐴 𝐴 PROPN ajst-5438 61 17 √ √ VERB ajst-5438 61 18 . . PUNCT ajst-5438 62 1 ， ， PROPN ajst-5438 62 2 𝐢 𝐢 PROPN ajst-5438 62 3 √ √ PROPN ajst-5438 62 4 . . PUNCT ajst-5438 62 5 . . PUNCT ajst-5438 63 1 in in ADP ajst-5438 63 2 addition addition NOUN ajst-5438 63 3 , , PUNCT ajst-5438 63 4 this this DET ajst-5438 63 5 paper paper NOUN ajst-5438 63 6 uses use VERB ajst-5438 63 7 the the DET ajst-5438 63 8 kernel kernel PROPN ajst-5438 63 9 function function NOUN ajst-5438 64 1 𝐾 𝐾 PROPN ajst-5438 64 2 π‘₯ π‘₯ PROPN ajst-5438 64 3 √ √ INTJ ajst-5438 65 1 𝑒π‘₯𝑝 𝑒π‘₯𝑝 INTJ ajst-5438 65 2 , , PUNCT ajst-5438 65 3 β„Ž β„Ž PROPN ajst-5438 65 4 is be AUX ajst-5438 65 5 the the DET ajst-5438 65 6 window window NOUN ajst-5438 65 7 width width NOUN ajst-5438 65 8 , , PUNCT ajst-5438 65 9 which which PRON ajst-5438 65 10 is be AUX ajst-5438 65 11 selected select VERB ajst-5438 65 12 by by ADP ajst-5438 65 13 the the DET ajst-5438 65 14 following follow VERB ajst-5438 65 15 generalized generalize VERB ajst-5438 65 16 cross cross NOUN ajst-5438 65 17 validation validation NOUN ajst-5438 65 18 method method NOUN ajst-5438 65 19 and and CCONJ ajst-5438 65 20 meets meet VERB ajst-5438 65 21 the the DET ajst-5438 65 22 assumption assumption NOUN ajst-5438 65 23 c6 c6 NOUN ajst-5438 65 24 : : PUNCT ajst-5438 65 25 𝐺𝐢𝑉 𝐺𝐢𝑉 NOUN ajst-5438 65 26 β„Ž β„Ž PROPN ajst-5438 65 27 1 1 NUM ajst-5438 65 28 𝑛 𝑛 DET ajst-5438 65 29 π‘Œ π‘Œ PROPN ajst-5438 65 30 𝑍 𝑍 VERB ajst-5438 65 31 πœƒ πœƒ NOUN ajst-5438 65 32 𝑔 𝑔 NOUN ajst-5438 65 33 𝑋 𝑋 PROPN ajst-5438 65 34 𝛽 𝛽 PROPN ajst-5438 65 35 𝑛 𝑛 PRON ajst-5438 65 36 π‘‘π‘Ÿ π‘‘π‘Ÿ VERB ajst-5438 65 37 𝐼 𝐼 PROPN ajst-5438 65 38 𝑆 𝑆 PROPN ajst-5438 65 39 for for ADP ajst-5438 65 40 the the DET ajst-5438 65 41 convenience convenience NOUN ajst-5438 65 42 of of ADP ajst-5438 65 43 comparison comparison NOUN ajst-5438 65 44 , , PUNCT ajst-5438 65 45 n n PRON ajst-5438 65 46 is be AUX ajst-5438 65 47 selected select VERB ajst-5438 65 48 as as ADP ajst-5438 65 49 50 50 NUM ajst-5438 65 50 " " PUNCT ajst-5438 65 51 , , PUNCT ajst-5438 65 52 " " PUNCT ajst-5438 65 53 150 150 NUM ajst-5438 65 54 and and CCONJ ajst-5438 65 55 200 200 NUM ajst-5438 65 56 respectively respectively ADV ajst-5438 65 57 , , PUNCT ajst-5438 65 58 and and CCONJ ajst-5438 65 59 the the DET ajst-5438 65 60 simulation simulation NOUN ajst-5438 65 61 results result NOUN ajst-5438 65 62 of of ADP ajst-5438 65 63 each each DET ajst-5438 65 64 case case NOUN ajst-5438 65 65 are be AUX ajst-5438 65 66 based base VERB ajst-5438 65 67 on on ADP ajst-5438 65 68 500 500 NUM ajst-5438 65 69 repeated repeat VERB ajst-5438 65 70 experiments experiment NOUN ajst-5438 65 71 . . PUNCT ajst-5438 66 1 in in ADP ajst-5438 66 2 this this DET ajst-5438 66 3 paper paper NOUN ajst-5438 66 4 , , PUNCT ajst-5438 66 5 the the DET ajst-5438 66 6 following follow VERB ajst-5438 66 7 evaluation evaluation NOUN ajst-5438 66 8 indicators indicator NOUN ajst-5438 66 9 are be AUX ajst-5438 66 10 used use VERB ajst-5438 66 11 to to PART ajst-5438 66 12 evaluate evaluate VERB ajst-5438 66 13 the the DET ajst-5438 66 14 accuracy accuracy NOUN ajst-5438 66 15 of of ADP ajst-5438 66 16 parameter parameter PROPN ajst-5438 66 17 estimation estimation NOUN ajst-5438 66 18 : : PUNCT ajst-5438 66 19 linear linear ADJ ajst-5438 66 20 parameter parameter NOUN ajst-5438 66 21 ΞΈ ΞΈ PROPN ajst-5438 66 22 estimator estimator NOUN ajst-5438 66 23 ΞΈ ΞΈ PROPN ajst-5438 66 24 Μ‚ Μ‚ PUNCT ajst-5438 66 25 deviation deviation NOUN ajst-5438 66 26 , , PUNCT ajst-5438 66 27 standard standard ADJ ajst-5438 66 28 deviation deviation NOUN ajst-5438 66 29 , , PUNCT ajst-5438 66 30 mean mean ADJ ajst-5438 66 31 square square ADJ ajst-5438 66 32 error error NOUN ajst-5438 66 33 and and CCONJ ajst-5438 66 34 index index NOUN ajst-5438 66 35 parameters parameter NOUN ajst-5438 66 36 of of ADP ajst-5438 66 37 Ξ² Ξ² PROPN ajst-5438 66 38 estimator estimator NOUN ajst-5438 66 39 Ξ² Ξ² PROPN ajst-5438 66 40 Μ‚ Μ‚ PUNCT ajst-5438 66 41 the the DET ajst-5438 66 42 deviation deviation NOUN ajst-5438 66 43 , , PUNCT ajst-5438 66 44 standard standard ADJ ajst-5438 66 45 deviation deviation NOUN ajst-5438 66 46 and and CCONJ ajst-5438 66 47 mean mean VERB ajst-5438 66 48 square square ADJ ajst-5438 66 49 error error NOUN ajst-5438 66 50 of of ADP ajst-5438 66 51 , , PUNCT ajst-5438 66 52 and and CCONJ ajst-5438 66 53 the the DET ajst-5438 66 54 estimator estimator NOUN ajst-5438 66 55 of of ADP ajst-5438 66 56 the the DET ajst-5438 66 57 linking link VERB ajst-5438 66 58 function function NOUN ajst-5438 66 59 g g PROPN ajst-5438 66 60 ( ( PUNCT ajst-5438 66 61 βˆ™ βˆ™ PROPN ajst-5438 66 62 ) ) PUNCT ajst-5438 66 63 g g NOUN ajst-5438 66 64 Μ‚ Μ‚ PUNCT ajst-5438 66 65 ( ( PUNCT ajst-5438 66 66 βˆ™ βˆ™ PROPN ajst-5438 66 67 ) ) PUNCT ajst-5438 66 68 the the DET ajst-5438 66 69 mean mean ADJ ajst-5438 66 70 and and CCONJ ajst-5438 66 71 standard standard ADJ ajst-5438 66 72 deviation deviation NOUN ajst-5438 66 73 of of ADP ajst-5438 66 74 rmse rmse NOUN ajst-5438 66 75 , , PUNCT ajst-5438 66 76 where where SCONJ ajst-5438 66 77 the the DET ajst-5438 66 78 estimated estimate VERB ajst-5438 66 79 rmse rmse NOUN ajst-5438 66 80 of of ADP ajst-5438 66 81 the the DET ajst-5438 66 82 connection connection NOUN ajst-5438 66 83 function function NOUN ajst-5438 66 84 g g PROPN ajst-5438 66 85 ( ( PUNCT ajst-5438 66 86 βˆ™ βˆ™ PROPN ajst-5438 66 87 ) ) PUNCT ajst-5438 66 88 is be AUX ajst-5438 66 89 calculated calculate VERB ajst-5438 66 90 by by ADP ajst-5438 66 91 the the DET ajst-5438 66 92 square square ADJ ajst-5438 66 93 root root NOUN ajst-5438 66 94 of of ADP ajst-5438 66 95 the the DET ajst-5438 66 96 following following ADJ ajst-5438 66 97 mean mean ADJ ajst-5438 66 98 square square ADJ ajst-5438 66 99 error error NOUN ajst-5438 66 100 : : PUNCT ajst-5438 66 101 rmse rmse PROPN ajst-5438 66 102 𝑔 𝑔 PROPN ajst-5438 66 103 1 1 NUM ajst-5438 66 104 π‘šπ‘› π‘šπ‘› NOUN ajst-5438 66 105 𝑔 𝑔 PROPN ajst-5438 66 106 𝑋 𝑋 PROPN ajst-5438 66 107 𝛽 𝛽 PROPN ajst-5438 66 108 𝑔 𝑔 PROPN ajst-5438 66 109 𝑋 𝑋 PROPN ajst-5438 66 110 𝛽 𝛽 PROPN ajst-5438 66 111 table table NOUN ajst-5438 66 112 1 1 NUM ajst-5438 66 113 below below ADV ajst-5438 66 114 shows show VERB ajst-5438 66 115 the the DET ajst-5438 66 116 deviation deviation NOUN ajst-5438 66 117 , , PUNCT ajst-5438 66 118 standard standard ADJ ajst-5438 66 119 deviation deviation NOUN ajst-5438 66 120 and and CCONJ ajst-5438 66 121 mean mean VERB ajst-5438 66 122 square square ADJ ajst-5438 66 123 error error NOUN ajst-5438 66 124 of of ADP ajst-5438 66 125 the the DET ajst-5438 66 126 estimator estimator NOUN ajst-5438 66 127 when when SCONJ ajst-5438 66 128 n n PRON ajst-5438 66 129 is be AUX ajst-5438 66 130 taken take VERB ajst-5438 66 131 as as ADP ajst-5438 66 132 50 50 NUM ajst-5438 66 133 " " PUNCT ajst-5438 66 134 , , PUNCT ajst-5438 66 135 " " PUNCT ajst-5438 66 136 150 150 NUM ajst-5438 66 137 " " PUNCT ajst-5438 66 138 and and CCONJ ajst-5438 66 139 200 200 NUM ajst-5438 66 140 respectively respectively ADV ajst-5438 66 141 . . PUNCT ajst-5438 67 1 figure figure NOUN ajst-5438 67 2 1 1 NUM ajst-5438 67 3 shows show VERB ajst-5438 67 4 the the DET ajst-5438 67 5 scatter scatter NOUN ajst-5438 67 6 diagram diagram NOUN ajst-5438 67 7 of of ADP ajst-5438 67 8 the the DET ajst-5438 67 9 connection connection NOUN ajst-5438 67 10 function function NOUN ajst-5438 67 11 when when SCONJ ajst-5438 67 12 n=50 n=50 ADJ ajst-5438 67 13 " " PUNCT ajst-5438 67 14 , , PUNCT ajst-5438 67 15 " " PUNCT ajst-5438 67 16 150 150 NUM ajst-5438 67 17 " " PUNCT ajst-5438 67 18 and and CCONJ ajst-5438 67 19 200 200 NUM ajst-5438 67 20 " " PUNCT ajst-5438 67 21 . . PUNCT ajst-5438 68 1 table table NOUN ajst-5438 68 2 1 1 NUM ajst-5438 68 3 . . X ajst-5438 69 1 𝛽 𝛽 NOUN ajst-5438 69 2 and and CCONJ ajst-5438 69 3 πœƒ πœƒ PRON ajst-5438 69 4 deviation deviation NOUN ajst-5438 69 5 , , PUNCT ajst-5438 69 6 standard standard ADJ ajst-5438 69 7 deviation deviation NOUN ajst-5438 69 8 and and CCONJ ajst-5438 69 9 mean mean VERB ajst-5438 69 10 square square ADJ ajst-5438 69 11 error error NOUN ajst-5438 69 12 of of ADP ajst-5438 69 13 estimator estimator NOUN ajst-5438 69 14 , , PUNCT ajst-5438 69 15 g g PROPN ajst-5438 69 16 ( ( PUNCT ajst-5438 69 17 Μ‚βˆ™ Μ‚βˆ™ NOUN ajst-5438 69 18 ) ) PUNCT ajst-5438 69 19 mean mean NOUN ajst-5438 69 20 and and CCONJ ajst-5438 69 21 standard standard ADJ ajst-5438 69 22 deviation deviation NOUN ajst-5438 69 23 of of ADP ajst-5438 69 24 rmse rmse NOUN ajst-5438 69 25 𝒏 𝒏 PROPN ajst-5438 69 26 150 150 NUM ajst-5438 69 27 200 200 NUM ajst-5438 69 28 300 300 NUM ajst-5438 69 29 bias bias NOUN ajst-5438 69 30 std std NOUN ajst-5438 69 31 ste ste PROPN ajst-5438 69 32 mse mse PROPN ajst-5438 69 33 bias bias PROPN ajst-5438 69 34 std std VERB ajst-5438 69 35 ste ste PROPN ajst-5438 69 36 mse mse PROPN ajst-5438 69 37 bias bias PROPN ajst-5438 69 38 std std VERB ajst-5438 69 39 ste ste PROPN ajst-5438 69 40 mse mse PROPN ajst-5438 69 41 ΞΈ ΞΈ PROPN ajst-5438 69 42 0.0035 0.0035 NUM ajst-5438 69 43 0.1274 0.1274 NUM ajst-5438 69 44 0.1278 0.1278 NUM ajst-5438 69 45 0.0163 0.0163 NUM ajst-5438 69 46 0.0024 0.0024 NUM ajst-5438 69 47 0.1026 0.1026 NUM ajst-5438 69 48 0.1131 0.1131 NUM ajst-5438 69 49 0.0125 0.0125 NUM ajst-5438 69 50 0.0017 0.0017 NUM ajst-5438 69 51 0.0894 0.0894 NUM ajst-5438 69 52 0.0921 0.0921 NUM ajst-5438 69 53 0.008 0.008 NUM ajst-5438 69 54 Ξ²1 Ξ²1 NOUN ajst-5438 69 55 0.0432 0.0432 NUM ajst-5438 69 56 0.2644 0.2644 NUM ajst-5438 69 57 0.251 0.251 NUM ajst-5438 69 58 0.0718 0.0718 NUM ajst-5438 69 59 0.0466 0.0466 NUM ajst-5438 69 60 0.2372 0.2372 NUM ajst-5438 69 61 0.2163 0.2163 NUM ajst-5438 69 62 0.0584 0.0584 NUM ajst-5438 69 63 0.0311 0.0311 NUM ajst-5438 69 64 0.1918 0.1918 NUM ajst-5438 69 65 0.1746 0.1746 NUM ajst-5438 69 66 0.0377 0.0377 NUM ajst-5438 69 67 Ξ²2 Ξ²2 VERB ajst-5438 69 68 0.0209 0.0209 NUM ajst-5438 69 69 0.1304 0.1304 NUM ajst-5438 69 70 0.1217 0.1217 NUM ajst-5438 69 71 0.0174 0.0174 NUM ajst-5438 69 72 0.0193 0.0193 NUM ajst-5438 69 73 0.1102 0.1102 NUM ajst-5438 69 74 0.1053 0.1053 NUM ajst-5438 69 75 0.0125 0.0125 NUM ajst-5438 69 76 0.0125 0.0125 NUM ajst-5438 69 77 0.0898 0.0898 NUM ajst-5438 70 1 0.0854 0.0854 NUM ajst-5438 70 2 0.0083 0.0083 NUM ajst-5438 70 3 Ξ²3 Ξ²3 PROPN ajst-5438 70 4 0.0414 0.0414 NUM ajst-5438 70 5 0.2144 0.2144 NUM ajst-5438 70 6 0.1996 0.1996 NUM ajst-5438 70 7 0.0477 0.0477 NUM ajst-5438 70 8 0.0413 0.0413 NUM ajst-5438 70 9 0.1956 0.1956 NUM ajst-5438 70 10 0.1764 0.1764 NUM ajst-5438 70 11 0.0506 0.0506 NUM ajst-5438 70 12 0.0264 0.0264 NUM ajst-5438 70 13 0.1611 0.1611 NUM ajst-5438 70 14 0.1443 0.1443 NUM ajst-5438 70 15 0.0267 0.0267 NUM ajst-5438 70 16 Ξ²4 Ξ²4 PROPN ajst-5438 70 17 0.0221 0.0221 NUM ajst-5438 70 18 0.2479 0.2479 NUM ajst-5438 70 19 0.2253 0.2253 NUM ajst-5438 70 20 0.0143 0.0143 NUM ajst-5438 70 21 0.0109 0.0109 NUM ajst-5438 70 22 0.2196 0.2196 NUM ajst-5438 70 23 0.1945 0.1945 NUM ajst-5438 71 1 0.0105 0.0105 NUM ajst-5438 71 2 0.0311 0.0311 NUM ajst-5438 71 3 0.1761 0.1761 NUM ajst-5438 71 4 0.0763 0.0763 NUM ajst-5438 71 5 0.0068 0.0068 NUM ajst-5438 71 6 Ξ²5 Ξ²5 VERB ajst-5438 71 7 0.0418 0.0418 NUM ajst-5438 71 8 0.2005 0.2005 NUM ajst-5438 71 9 0.1793 0.1793 NUM ajst-5438 71 10 0.0419 0.0419 NUM ajst-5438 71 11 0.0432 0.0432 NUM ajst-5438 71 12 0.1002 0.1002 NUM ajst-5438 71 13 0.0939 0.0939 NUM ajst-5438 71 14 0.0352 0.0352 NUM ajst-5438 71 15 0.0138 0.0138 NUM ajst-5438 71 16 0.0815 0.0815 NUM ajst-5438 71 17 0.1302 0.1302 NUM ajst-5438 71 18 0.0225 0.0225 NUM ajst-5438 71 19 me i PRON ajst-5438 71 20 se se X ajst-5438 71 21 me i PRON ajst-5438 71 22 se se PROPN ajst-5438 71 23 me i PRON ajst-5438 71 24 se se ADV ajst-5438 71 25 g g ADP ajst-5438 71 26 0.0412 0.0412 NUM ajst-5438 71 27 0.0142 0.0142 NUM ajst-5438 71 28 0.0333 0.0333 NUM ajst-5438 71 29 0.0121 0.0121 NUM ajst-5438 71 30 0.0296 0.0296 NUM ajst-5438 71 31 0.0076 0.0076 NUM ajst-5438 71 32 figure figure NOUN ajst-5438 71 33 1 1 NUM ajst-5438 71 34 . . PUNCT ajst-5438 71 35 scatter scatter NOUN ajst-5438 71 36 diagram diagram NOUN ajst-5438 71 37 of of ADP ajst-5438 71 38 real real ADJ ajst-5438 71 39 connection connection NOUN ajst-5438 71 40 function function NOUN ajst-5438 71 41 and and CCONJ ajst-5438 71 42 estimated estimate VERB ajst-5438 71 43 connection connection NOUN ajst-5438 71 44 function function NOUN ajst-5438 71 45 when when SCONJ ajst-5438 71 46 n=50,100,200 n=50,100,200 PROPN ajst-5438 71 47 from from ADP ajst-5438 71 48 table table NOUN ajst-5438 71 49 1 1 NUM ajst-5438 71 50 and and CCONJ ajst-5438 71 51 figure figure NOUN ajst-5438 71 52 1 1 NUM ajst-5438 71 53 , , PUNCT ajst-5438 71 54 the the DET ajst-5438 71 55 following follow VERB ajst-5438 71 56 conclusions conclusion NOUN ajst-5438 71 57 can can AUX ajst-5438 71 58 be be AUX ajst-5438 71 59 drawn draw VERB ajst-5438 71 60 : : PUNCT ajst-5438 71 61 the the DET ajst-5438 71 62 deviation deviation NOUN ajst-5438 71 63 of of ADP ajst-5438 71 64 parameter parameter NOUN ajst-5438 71 65 estimation estimation NOUN ajst-5438 71 66 , , PUNCT ajst-5438 71 67 standard standard ADJ ajst-5438 71 68 error error NOUN ajst-5438 71 69 , , PUNCT ajst-5438 71 70 mean mean VERB ajst-5438 71 71 and and CCONJ ajst-5438 71 72 mean mean VERB ajst-5438 71 73 square square ADJ ajst-5438 71 74 error error NOUN ajst-5438 71 75 of of ADP ajst-5438 71 76 standard standard ADJ ajst-5438 71 77 error error NOUN ajst-5438 71 78 , , PUNCT ajst-5438 71 79 as as ADV ajst-5438 71 80 well well ADV ajst-5438 71 81 as as ADP ajst-5438 71 82 the the DET ajst-5438 71 83 mean mean ADJ ajst-5438 71 84 and and CCONJ ajst-5438 71 85 standard standard ADJ ajst-5438 71 86 error error NOUN ajst-5438 71 87 of of ADP ajst-5438 71 88 rase rase PROPN ajst-5438 71 89 estimated estimate VERB ajst-5438 71 90 by by ADP ajst-5438 71 91 the the DET ajst-5438 71 92 connection connection NOUN ajst-5438 71 93 function function NOUN ajst-5438 71 94 all all PRON ajst-5438 71 95 decreased decrease VERB ajst-5438 71 96 significantly significantly ADV ajst-5438 71 97 with with ADP ajst-5438 71 98 the the DET ajst-5438 71 99 115 115 NUM ajst-5438 71 100 increase increase NOUN ajst-5438 71 101 of of ADP ajst-5438 71 102 samples sample NOUN ajst-5438 71 103 . . PUNCT ajst-5438 72 1 therefore therefore ADV ajst-5438 72 2 , , PUNCT ajst-5438 72 3 the the DET ajst-5438 72 4 " " PUNCT ajst-5438 72 5 two two NUM ajst-5438 72 6 - - PUNCT ajst-5438 72 7 stage stage NOUN ajst-5438 72 8 estimation estimation NOUN ajst-5438 72 9 method method NOUN ajst-5438 72 10 " " PUNCT ajst-5438 72 11 proposed propose VERB ajst-5438 72 12 in in ADP ajst-5438 72 13 this this DET ajst-5438 72 14 paper paper NOUN ajst-5438 72 15 is be AUX ajst-5438 72 16 relatively relatively ADV ajst-5438 72 17 stable stable ADJ ajst-5438 72 18 in in ADP ajst-5438 72 19 the the DET ajst-5438 72 20 estimation estimation NOUN ajst-5438 72 21 of of ADP ajst-5438 72 22 parameters parameter NOUN ajst-5438 72 23 , , PUNCT ajst-5438 72 24 and and CCONJ ajst-5438 72 25 the the DET ajst-5438 72 26 connection connection NOUN ajst-5438 72 27 function function NOUN ajst-5438 72 28 estimation estimation NOUN ajst-5438 72 29 and and CCONJ ajst-5438 72 30 the the DET ajst-5438 72 31 fitting fitting ADJ ajst-5438 72 32 effect effect NOUN ajst-5438 72 33 of of ADP ajst-5438 72 34 the the DET ajst-5438 72 35 real real ADJ ajst-5438 72 36 curve curve NOUN ajst-5438 72 37 are be AUX ajst-5438 72 38 good good ADJ ajst-5438 72 39 . . PUNCT ajst-5438 73 1 4 4 X ajst-5438 73 2 . . X ajst-5438 73 3 conclusion conclusion NOUN ajst-5438 73 4 this this DET ajst-5438 73 5 paper paper NOUN ajst-5438 73 6 presents present VERB ajst-5438 73 7 a a DET ajst-5438 73 8 new new ADJ ajst-5438 73 9 " " PUNCT ajst-5438 73 10 two two NUM ajst-5438 73 11 - - PUNCT ajst-5438 73 12 stage stage NOUN ajst-5438 73 13 estimation estimation NOUN ajst-5438 73 14 method method NOUN ajst-5438 73 15 " " PUNCT ajst-5438 73 16 , , PUNCT ajst-5438 73 17 which which PRON ajst-5438 73 18 is be AUX ajst-5438 73 19 based base VERB ajst-5438 73 20 on on ADP ajst-5438 73 21 local local ADJ ajst-5438 73 22 polynomial polynomial ADJ ajst-5438 73 23 and and CCONJ ajst-5438 73 24 bias bias NOUN ajst-5438 73 25 correction correction NOUN ajst-5438 73 26 generalized generalize VERB ajst-5438 73 27 estimation estimation NOUN ajst-5438 73 28 equation equation NOUN ajst-5438 73 29 . . PUNCT ajst-5438 74 1 it it PRON ajst-5438 74 2 can can AUX ajst-5438 74 3 estimate estimate VERB ajst-5438 74 4 the the DET ajst-5438 74 5 index index NOUN ajst-5438 74 6 parameters parameter NOUN ajst-5438 74 7 and and CCONJ ajst-5438 74 8 linear linear ADJ ajst-5438 74 9 parameters parameter NOUN ajst-5438 74 10 in in ADP ajst-5438 74 11 turn turn NOUN ajst-5438 74 12 , , PUNCT ajst-5438 74 13 and and CCONJ ajst-5438 74 14 can can AUX ajst-5438 74 15 obtain obtain VERB ajst-5438 74 16 the the DET ajst-5438 74 17 asymptotic asymptotic ADJ ajst-5438 74 18 normality normality NOUN ajst-5438 74 19 of of ADP ajst-5438 74 20 the the DET ajst-5438 74 21 estimator estimator NOUN ajst-5438 74 22 . . PUNCT ajst-5438 75 1 the the DET ajst-5438 75 2 monte monte PROPN ajst-5438 75 3 carlo carlo PROPN ajst-5438 75 4 simulation simulation PROPN ajst-5438 75 5 results result NOUN ajst-5438 75 6 show show VERB ajst-5438 75 7 that that SCONJ ajst-5438 75 8 the the DET ajst-5438 75 9 algorithm algorithm NOUN ajst-5438 75 10 has have VERB ajst-5438 75 11 good good ADJ ajst-5438 75 12 robustness robustness NOUN ajst-5438 75 13 . . PUNCT ajst-5438 76 1 references reference NOUN ajst-5438 76 2 [ [ X ajst-5438 76 3 1 1 NUM ajst-5438 76 4 ] ] PUNCT ajst-5438 76 5 shakhawat shakhawat PROPN ajst-5438 76 6 hossain hossain PROPN ajst-5438 76 7 and and CCONJ ajst-5438 76 8 le le PRON ajst-5438 76 9 an an DET ajst-5438 76 10 lac lac PROPN ajst-5438 76 11 . . PUNCT ajst-5438 77 1 optimal optimal ADJ ajst-5438 77 2 shrinkage shrinkage NOUN ajst-5438 77 3 estimations estimation NOUN ajst-5438 77 4 in in ADP ajst-5438 77 5 partially partially ADV ajst-5438 77 6 linear linear ADJ ajst-5438 77 7 single single ADJ ajst-5438 77 8 - - PUNCT ajst-5438 77 9 index index NOUN ajst-5438 77 10 models model NOUN ajst-5438 77 11 for for ADP ajst-5438 77 12 binary binary PROPN ajst-5438 77 13 longitudinal longitudinal ADJ ajst-5438 77 14 data[j data[j PROPN ajst-5438 77 15 ] ] PUNCT ajst-5438 77 16 . . PUNCT ajst-5438 78 1 test test NOUN ajst-5438 78 2 , , PUNCT ajst-5438 78 3 2021 2021 NUM ajst-5438 78 4 , , PUNCT ajst-5438 78 5 30(4 30(4 NUM ajst-5438 78 6 ) ) PUNCT ajst-5438 78 7 : : PUNCT ajst-5438 78 8 1 1 NUM ajst-5438 78 9 - - SYM ajst-5438 78 10 25 25 NUM ajst-5438 78 11 . . PUNCT ajst-5438 79 1 [ [ X ajst-5438 79 2 2 2 NUM ajst-5438 79 3 ] ] X ajst-5438 79 4 quan quan PROPN ajst-5438 79 5 cai cai PROPN ajst-5438 79 6 and and CCONJ ajst-5438 79 7 suojin suojin PROPN ajst-5438 79 8 wang wang PROPN ajst-5438 79 9 . . PUNCT ajst-5438 80 1 inferences inference NOUN ajst-5438 80 2 with with ADP ajst-5438 80 3 generalized generalize VERB ajst-5438 80 4 partially partially ADV ajst-5438 80 5 linear linear VERB ajst-5438 80 6 single single ADJ ajst-5438 80 7 - - PUNCT ajst-5438 80 8 index index NOUN ajst-5438 80 9 models model NOUN ajst-5438 80 10 for for ADP ajst-5438 80 11 longitaudinal longitaudinal ADJ ajst-5438 80 12 dta[j dta[j NOUN ajst-5438 80 13 ] ] PUNCT ajst-5438 80 14 . . PUNCT ajst-5438 81 1 journal journal PROPN ajst-5438 81 2 of of ADP ajst-5438 81 3 statistical statistical ADJ ajst-5438 81 4 planning planning NOUN ajst-5438 81 5 and and CCONJ ajst-5438 81 6 inference inference NOUN ajst-5438 81 7 , , PUNCT ajst-5438 81 8 2018 2018 NUM ajst-5438 81 9 , , PUNCT ajst-5438 81 10 200 200 NUM ajst-5438 81 11 : : SYM ajst-5438 81 12 146160 146160 NUM ajst-5438 81 13 . . PUNCT ajst-5438 82 1 [ [ X ajst-5438 82 2 3 3 X ajst-5438 82 3 ] ] X ajst-5438 82 4 gaorong gaorong PROPN ajst-5438 82 5 li li PROPN ajst-5438 82 6 and and CCONJ ajst-5438 82 7 peng peng PROPN ajst-5438 82 8 lai lai PROPN ajst-5438 82 9 and and CCONJ ajst-5438 82 10 heng heng PROPN ajst-5438 82 11 lian lian PROPN ajst-5438 82 12 . . PUNCT ajst-5438 82 13 variable variable ADJ ajst-5438 82 14 selection selection NOUN ajst-5438 82 15 and and CCONJ ajst-5438 82 16 estimation estimation NOUN ajst-5438 82 17 for for ADP ajst-5438 82 18 partially partially ADV ajst-5438 82 19 linear linear ADJ ajst-5438 82 20 single single ADJ ajst-5438 82 21 - - PUNCT ajst-5438 82 22 index index NOUN ajst-5438 82 23 models model NOUN ajst-5438 82 24 with with ADP ajst-5438 82 25 longitudinal longitudinal ADJ ajst-5438 82 26 data[j data[j NOUN ajst-5438 82 27 ] ] PUNCT ajst-5438 82 28 . . PUNCT ajst-5438 83 1 statistics statistic NOUN ajst-5438 83 2 and and CCONJ ajst-5438 83 3 computing computing NOUN ajst-5438 83 4 , , PUNCT ajst-5438 83 5 2015,25(3 2015,25(3 PROPN ajst-5438 83 6 ) ) PUNCT ajst-5438 83 7 : : PUNCT ajst-5438 83 8 579 579 NUM ajst-5438 83 9 - - SYM ajst-5438 83 10 593 593 NUM ajst-5438 83 11 . . PUNCT ajst-5438 84 1 [ [ X ajst-5438 84 2 4 4 X ajst-5438 84 3 ] ] X ajst-5438 84 4 peng peng PROPN ajst-5438 84 5 lai lai PROPN ajst-5438 84 6 and and CCONJ ajst-5438 84 7 gaorong gaorong PROPN ajst-5438 84 8 li li PROPN ajst-5438 84 9 and and CCONJ ajst-5438 84 10 heng heng PROPN ajst-5438 84 11 lian lian PROPN ajst-5438 84 12 . . PUNCT ajst-5438 84 13 quadratic quadratic ADJ ajst-5438 84 14 inference inference NOUN ajst-5438 84 15 functions function NOUN ajst-5438 84 16 for for ADP ajst-5438 84 17 partially partially ADV ajst-5438 84 18 linear linear ADJ ajst-5438 84 19 single single ADJ ajst-5438 84 20 - - PUNCT ajst-5438 84 21 index index NOUN ajst-5438 84 22 models model NOUN ajst-5438 84 23 with with ADP ajst-5438 84 24 longitudinal longitudinal ADJ ajst-5438 84 25 data[j data[j NOUN ajst-5438 84 26 ] ] PUNCT ajst-5438 84 27 . . PUNCT ajst-5438 85 1 journal journal PROPN ajst-5438 85 2 of of ADP ajst-5438 85 3 multivariate multivariate NOUN ajst-5438 85 4 analysis analysis NOUN ajst-5438 85 5 , , PUNCT ajst-5438 85 6 2013 2013 NUM ajst-5438 85 7 , , PUNCT ajst-5438 85 8 118 118 NUM ajst-5438 85 9 : : SYM ajst-5438 85 10 115 115 NUM ajst-5438 85 11 - - SYM ajst-5438 85 12 127 127 NUM ajst-5438 85 13 . . PUNCT ajst-5438 86 1 [ [ X ajst-5438 86 2 5 5 X ajst-5438 86 3 ] ] PUNCT ajst-5438 86 4 zeger zeger NOUN ajst-5438 86 5 s s PART ajst-5438 86 6 l l NOUN ajst-5438 86 7 , , PUNCT ajst-5438 86 8 diggle diggle PROPN ajst-5438 86 9 p p PROPN ajst-5438 86 10 j. j. PROPN ajst-5438 86 11 semiparametric semiparametric PROPN ajst-5438 86 12 models model NOUN ajst-5438 86 13 for for ADP ajst-5438 86 14 longitudinal longitudinal ADJ ajst-5438 86 15 data datum NOUN ajst-5438 86 16 with with ADP ajst-5438 86 17 application application NOUN ajst-5438 86 18 to to ADP ajst-5438 86 19 cd4 cd4 PROPN ajst-5438 86 20 cell cell NOUN ajst-5438 86 21 numbers number NOUN ajst-5438 86 22 in in ADP ajst-5438 86 23 hiv hiv PROPN ajst-5438 86 24 seroconverters seroconverter NOUN ajst-5438 86 25 . . PUNCT ajst-5438 87 1 biometrics biometric NOUN ajst-5438 87 2 , , PUNCT ajst-5438 87 3 1994 1994 NUM ajst-5438 87 4 , , PUNCT ajst-5438 87 5 50 50 NUM ajst-5438 87 6 : : PUNCT ajst-5438 87 7 689–699 689–699 NUM ajst-5438 87 8 . . PUNCT ajst-5438 88 1 [ [ X ajst-5438 88 2 6 6 NUM ajst-5438 88 3 ] ] PUNCT ajst-5438 88 4 yu yu PROPN ajst-5438 88 5 ying ying PROPN ajst-5438 88 6 jiang jiang PROPN ajst-5438 88 7 . . PUNCT ajst-5438 89 1 empirical empirical ADJ ajst-5438 89 2 likelihood likelihood NOUN ajst-5438 89 3 inference inference NOUN ajst-5438 89 4 for for ADP ajst-5438 89 5 a a DET ajst-5438 89 6 partially partially ADV ajst-5438 89 7 linear linear ADJ ajst-5438 89 8 model model NOUN ajst-5438 89 9 under under ADP ajst-5438 89 10 longitudinal longitudinal ADJ ajst-5438 89 11 data[j data[j NOUN ajst-5438 89 12 ] ] PUNCT ajst-5438 89 13 . . PUNCT ajst-5438 90 1 applied apply VERB ajst-5438 90 2 mechanics mechanic NOUN ajst-5438 90 3 and and CCONJ ajst-5438 90 4 materials material NOUN ajst-5438 90 5 , , PUNCT ajst-5438 90 6 2013 2013 NUM ajst-5438 90 7 , , PUNCT ajst-5438 90 8 2545(353 2545(353 NUM ajst-5438 90 9 - - SYM ajst-5438 90 10 356 356 NUM ajst-5438 90 11 ) ) PUNCT ajst-5438 90 12 : : PUNCT ajst-5438 90 13 3355 3355 NUM ajst-5438 90 14 - - SYM ajst-5438 90 15 3358 3358 NUM ajst-5438 90 16 . . PUNCT ajst-5438 91 1 [ [ X ajst-5438 91 2 7 7 X ajst-5438 91 3 ] ] PUNCT ajst-5438 91 4 hongmei hongmei PROPN ajst-5438 91 5 lin lin PROPN ajst-5438 91 6 et et PROPN ajst-5438 91 7 al al PROPN ajst-5438 91 8 . . PUNCT ajst-5438 92 1 a a DET ajst-5438 92 2 new new ADJ ajst-5438 92 3 local local ADJ ajst-5438 92 4 estimation estimation NOUN ajst-5438 92 5 method method NOUN ajst-5438 92 6 for for ADP ajst-5438 92 7 single single ADJ ajst-5438 92 8 index index NOUN ajst-5438 92 9 models model NOUN ajst-5438 92 10 for for ADP ajst-5438 92 11 longitudinal longitudinal ADJ ajst-5438 92 12 data[j data[j NOUN ajst-5438 92 13 ] ] PUNCT ajst-5438 92 14 . . PUNCT ajst-5438 93 1 journal journal PROPN ajst-5438 93 2 of of ADP ajst-5438 93 3 nonparametric nonparametric PROPN ajst-5438 93 4 statistics statistic NOUN ajst-5438 93 5 , , PUNCT ajst-5438 93 6 2016 2016 NUM ajst-5438 93 7 , , PUNCT ajst-5438 93 8 28(3 28(3 NUM ajst-5438 93 9 ) ) PUNCT ajst-5438 93 10 : : PUNCT ajst-5438 94 1 644 644 NUM ajst-5438 94 2 - - SYM ajst-5438 94 3 658 658 NUM ajst-5438 94 4 . . PUNCT ajst-5438 95 1 [ [ X ajst-5438 95 2 8 8 NUM ajst-5438 95 3 ] ] X ajst-5438 95 4 peng peng PROPN ajst-5438 95 5 lai lai PROPN ajst-5438 95 6 and and CCONJ ajst-5438 95 7 gaorong gaorong PROPN ajst-5438 95 8 li li PROPN ajst-5438 95 9 and and CCONJ ajst-5438 95 10 heng heng PROPN ajst-5438 95 11 lian lian PROPN ajst-5438 95 12 . . PROPN ajst-5438 96 1 semiparametric semiparametric PROPN ajst-5438 96 2 estimation estimation NOUN ajst-5438 96 3 of of ADP ajst-5438 96 4 fixed fix VERB ajst-5438 96 5 effects effect NOUN ajst-5438 96 6 panel panel NOUN ajst-5438 96 7 data data VERB ajst-5438 96 8 single single ADJ ajst-5438 96 9 - - PUNCT ajst-5438 96 10 index index NOUN ajst-5438 96 11 model[j model[j PROPN ajst-5438 96 12 ] ] X ajst-5438 96 13 . . PUNCT ajst-5438 97 1 statistics statistic NOUN ajst-5438 97 2 and and CCONJ ajst-5438 97 3 probability probability NOUN ajst-5438 97 4 letters letter NOUN ajst-5438 97 5 , , PUNCT ajst-5438 97 6 2013 2013 NUM ajst-5438 97 7 , , PUNCT ajst-5438 97 8 83(6 83(6 NOUN ajst-5438 97 9 ) ) PUNCT ajst-5438 97 10 : : PUNCT ajst-5438 97 11 1595 1595 NUM ajst-5438 97 12 - - SYM ajst-5438 97 13 1602 1602 NUM ajst-5438 97 14 . . PUNCT ajst-5438 98 1 [ [ X ajst-5438 98 2 9 9 NUM ajst-5438 98 3 ] ] PUNCT ajst-5438 98 4 ruiqin ruiqin VERB ajst-5438 98 5 tian tian NOUN ajst-5438 98 6 and and CCONJ ajst-5438 98 7 liugen liugen PROPN ajst-5438 98 8 xue xue PROPN ajst-5438 98 9 . . PUNCT ajst-5438 99 1 generalized generalize VERB ajst-5438 99 2 empirical empirical ADJ ajst-5438 99 3 likelihood likelihood NOUN ajst-5438 99 4 inference inference NOUN ajst-5438 99 5 in in ADP ajst-5438 99 6 partial partial ADJ ajst-5438 99 7 linear linear PROPN ajst-5438 99 8 regression regression NOUN ajst-5438 99 9 model model NOUN ajst-5438 99 10 for for ADP ajst-5438 99 11 longitudinal longitudinal ADJ ajst-5438 99 12 data[j data[j NOUN ajst-5438 99 13 ] ] X ajst-5438 99 14 . . PUNCT ajst-5438 100 1 statistics statistic NOUN ajst-5438 100 2 , , PUNCT ajst-5438 100 3 2017 2017 NUM ajst-5438 100 4 , , PUNCT ajst-5438 100 5 51(5 51(5 NUM ajst-5438 100 6 ) ) PUNCT ajst-5438 100 7 : : PUNCT ajst-5438 100 8 988 988 NUM ajst-5438 100 9 - - SYM ajst-5438 100 10 1005 1005 NUM ajst-5438 100 11 . . PUNCT ajst-5438 101 1 [ [ X ajst-5438 101 2 10 10 NUM ajst-5438 101 3 ] ] X ajst-5438 101 4 xue xue PROPN ajst-5438 101 5 l l PROPN ajst-5438 101 6 g g PROPN ajst-5438 101 7 , , PUNCT ajst-5438 101 8 zhu zhu PROPN ajst-5438 101 9 l. l. PROPN ajst-5438 101 10 empirical empirical ADJ ajst-5438 101 11 likelihood likelihood NOUN ajst-5438 101 12 for for ADP ajst-5438 101 13 single single ADJ ajst-5438 101 14 - - PUNCT ajst-5438 101 15 index index NOUN ajst-5438 101 16 models model NOUN ajst-5438 101 17 . . PUNCT ajst-5438 102 1 j j PROPN ajst-5438 102 2 multivariate multivariate PROPN ajst-5438 102 3 anal anal NOUN ajst-5438 102 4 , , PUNCT ajst-5438 102 5 2006 2006 NUM ajst-5438 102 6 , , PUNCT ajst-5438 102 7 97 97 NUM ajst-5438 102 8 : : SYM ajst-5438 102 9 1295–1312 1295–1312 NUM ajst-5438 102 10 . . PUNCT ajst-5438 103 1 [ [ X ajst-5438 103 2 11 11 NUM ajst-5438 103 3 ] ] X ajst-5438 103 4 chen chen PROPN ajst-5438 103 5 j j PROPN ajst-5438 103 6 , , PUNCT ajst-5438 103 7 li li PROPN ajst-5438 103 8 d d PROPN ajst-5438 103 9 , , PUNCT ajst-5438 103 10 liang liang PROPN ajst-5438 103 11 h h PROPN ajst-5438 103 12 , , PUNCT ajst-5438 103 13 et et PROPN ajst-5438 103 14 al al PROPN ajst-5438 103 15 . . PROPN ajst-5438 103 16 semiparametric semiparametric PROPN ajst-5438 103 17 gee gee NOUN ajst-5438 103 18 analysis analysis NOUN ajst-5438 103 19 in in ADP ajst-5438 103 20 partially partially ADV ajst-5438 103 21 linear linear ADJ ajst-5438 103 22 single single ADJ ajst-5438 103 23 - - PUNCT ajst-5438 103 24 index index NOUN ajst-5438 103 25 models model NOUN ajst-5438 103 26 for for ADP ajst-5438 103 27 longitudinal longitudinal ADJ ajst-5438 103 28 data datum NOUN ajst-5438 103 29 . . PUNCT ajst-5438 104 1 ann ann PROPN ajst-5438 104 2 statist statist PROPN ajst-5438 104 3 , , PUNCT ajst-5438 104 4 2015 2015 NUM ajst-5438 104 5 , , PUNCT ajst-5438 104 6 43 43 NUM ajst-5438 104 7 : : SYM ajst-5438 104 8 1682–1715 1682–1715 NUM ajst-5438 104 9 . . PUNCT ajst-5438 105 1 [ [ X ajst-5438 105 2 12 12 NUM ajst-5438 105 3 ] ] X ajst-5438 105 4 pang pang NOUN ajst-5438 105 5 z z PROPN ajst-5438 105 6 , , PUNCT ajst-5438 105 7 xue xue PROPN ajst-5438 105 8 l. l. PROPN ajst-5438 105 9 estimation estimation PROPN ajst-5438 105 10 for for ADP ajst-5438 105 11 the the DET ajst-5438 105 12 single single ADJ ajst-5438 105 13 - - PUNCT ajst-5438 105 14 index index NOUN ajst-5438 105 15 models model NOUN ajst-5438 105 16 with with ADP ajst-5438 105 17 random random ADJ ajst-5438 105 18 effects effect NOUN ajst-5438 105 19 . . PUNCT ajst-5438 106 1 comput comput ADJ ajst-5438 106 2 statist statist ADJ ajst-5438 106 3 data data PROPN ajst-5438 106 4 anal anal NOUN ajst-5438 106 5 , , PUNCT ajst-5438 106 6 2012 2012 NUM ajst-5438 106 7 , , PUNCT ajst-5438 106 8 56 56 NUM ajst-5438 106 9 : : SYM ajst-5438 106 10 1837 1837 NUM ajst-5438 106 11 – – PUNCT ajst-5438 106 12 1853 1853 NUM ajst-5438 106 13 . . PUNCT