id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ma-142	Bishwal, Jaya P. N.	On the Kolmogorov Distance for the Least Squares Estimator in the Fractional Ornstein-Uhlenbeck Process	2023	17	.pdf	application/pdf	5508	335	84	IT − 2H ( T −σ2H θ̃T )1/2 σ2Hb0θx ⇒ 2H ( T −σ2H θ̃T )1/2 (θ̃T − θ)[IT − b0T (θT − θ)] > x IT − 2H ( T −σ2H θ̃T )1/2 2b0θx  ⇒ (θ̃T − θ)IT − b0T (θ̃T − θ)2 > ( −σ2Hθ 4TH2 )1/2 IT x − σ2Hb0θx2 ⇒ −NT + (θ̃T − θ)IT − b0T (θT − θ)2 > −NT + ( −σ2Hθ 4TH2 )1/2 IT x − σ2Hb0θx2 ⇒ 0 > −NT + ( −σ2Hθ 4TH2 )1/2 IT x − σ2Hb0θx2 since IT − b0T (θ̃T − θ) > Tc0 − b0T (θ̃T − θ) > 2σ2Hb0(logT )1/2 ( −σ2Hθ 4TH2 )1/2 − σ2Hb0(logT )1/2 ( −σ2Hθ 4TH2 )1/2 = σ2Hb0(logT )1/2 ( −σ2Hθ 4TH2 )1/2 > 0. [IT − ( T −σ2H θ̃T )1/2 σ2Hb0θx ] ⇒ (θ̂T − θ)IT − b0T (θ̂T − θ)2 > ( T −σ2H θ̃T )−1/2 IT x − σ2Hb0θx2 ⇒ −MT + (θ̂T − θ)IT − b0T (θ̂T − θ)2 > −MT + ( T −σ2H θ̃T )−1/2 IT x − σ2Hb0θx2 ⇒ 0 > −MT + ( −σ2H θ̃T T )1/2 IT x − σ2Hb0θx2 since IT − b0T (θ̂T − θ) > Tc0 − b0T (θ̂T − θ) > 2σ2Hb0(logT )1/2 ( −σ2H θ̃T T )1/2 − σ2Hb0(logT )1/2 ( −σ2H θ̃T T )1/2 = σ2Hb0(logT )1/2 ( −σ2H θ̃T T )1/2 > 0.	cache/ma-142.pdf	txt/ma-142.txt
