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Large and moderate deviation principles for the bootstrap sample quantile
Yu Miao,Jianyong Mu,Jinghuan Zhao,Saralees Nadarajah 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.4
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 {X∗ n,1, · · · , X∗ n,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 quantileξ ∗ np are established.