id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4765	Modou Kebe; Deme, El Hadji; Tchilabalo Abozou Kpanzou; Manou-Abi, Solym Mawaki; Ebrima Sisawo	Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions	2023	35	.pdf	application/pdf	13726	705	77	− k/n, Un,k,2 ( Q (K) n,k ) := ∫ 1 1−k/n Q (K) n,k (s)ds = (k/n)Xn−k,n 1 − γ̂ (K) n,k . with Qn(·) (respectively, Q (K) n,k is the empirical estimator (respectively, the Weissman’s type estimator) of the quantile function Q(·) and k = k(n) is a sequence of integers satis- fying k → ∞, k/n → 0 and as n → ∞. To simplify the proof, we need the following preliminary results whose proofs are given after this one. − Un,k,1(Q, β) L(Q,α) } (k/n)1/2Xn−k,n d = Wn,α,1 + oP(1), (19) as n → ∞, where Wn,α,1 := − ∫ 1−k/n 0 Bn(s)dQ(s) L(Q,α) (k/n)1/2Q(1 − k/n) .	cache/ejpam-4765.pdf	txt/ejpam-4765.txt