Large and moderate deviation principles for the bootstrap sample quantile

Abstract

Let {X,Xn,n≥1} be a sequence of independent identically distributed (i.i.d.) random variables defined on a probability space (Ω,F,P) with common distribution F, and let {Xn,1∗,⋯,Xn,n∗} be a bootstrap sample from the empirical distribution Fn. Based on the bootstrap sample, the moderate deviation, large deviation and Bahadur’s asymptotic efficiency of the bootstrap sample pth quantile ξ̂np∗ are established.