id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6024	Deme, El Hadji; Agbrabatt, Aminetou; Barry, Mamadou Aliou; Ahmedou, Sidiya; El Waled, Khalil	A Class of Reduced Bias Estimators of Distortion Risk Measures under Dependence Serials with Heavy-Tailed Marginals	2025	25	.pdf	application/pdf	11442	551	74	The first part ( n k s )−γ Q(1 − k/n) in the right side of (18) is exactly estimated by the Weissman’s type estimator Q̂ (K) k (1 − s) and defined in (12). − γ 1 β − γ  gβ(k/n)Xn−k,n H2 = γ 1 β − γ ( Xn−k,n Q(1− k/n) − 1 ) gβ(k/n)Q(1− k/n) H3 = γ 1 β − γ gβ(k/n)Q(1− k/n)− ∫ ∞ Q(1−k/n) gβ(F (x))dx H4 = Ân,k(ρ̂ )( 1 β − γ̂ (K∆̂∗ opt ) n,k )( 1− βγ̂ (K∆̂∗ opt ) n,k − βρ̂ )gβ(k/n) Xn−k,n. Under assumptions and for all n large enough, we have from (23), √ k ( γ̂ (K∆̂∗ opt ) k	cache/ejpam-6024.pdf	txt/ejpam-6024.txt