Large and moderate deviation principles for the bootstrap sample quantile

Chao Yu Miao; Jianyong Mu; Jinghuan Zhao; Saralees Nadarajah

doi:10.1016/j.jkss.2017.04.003

Large and moderate deviation principles for the bootstrap sample quantile

Chao Yu Miao, Jianyong Mu, Jinghuan Zhao, Saralees Nadarajah

Henan Normal University

Research output: Contribution to journal › Article › peer-review

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 ξˆnp* are established.

Original language	English
Journal	Journal of the Korean Statistical Society
Volume	46
Issue number	4
Early online date	30 May 2017
DOIs	https://doi.org/10.1016/j.jkss.2017.04.003
Publication status	Published - 2017

Keywords

60F10
62G30
Bahadur's asymptotic efficiency
Bootstrap
Large deviation
Moderate deviation
Sample quantile

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10.1016/j.jkss.2017.04.003

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title = "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 ξˆnp* are established.",

keywords = "60F10, 62G30, Bahadur's asymptotic efficiency, Bootstrap, Large deviation, Moderate deviation, Sample quantile",

author = "Miao, {Chao Yu} and Jianyong Mu and Jinghuan Zhao and Saralees Nadarajah",

year = "2017",

doi = "10.1016/j.jkss.2017.04.003",

language = "English",

volume = "46",

journal = "Journal of the Korean Statistical Society",

issn = "1226-3192",

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TY - JOUR

T1 - Large and moderate deviation principles for the bootstrap sample quantile

AU - Miao, Chao Yu

AU - Mu, Jianyong

AU - Zhao, Jinghuan

AU - Nadarajah, Saralees

PY - 2017

Y1 - 2017

N2 - 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 ξˆnp* are established.

AB - 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 ξˆnp* are established.

KW - 60F10

KW - 62G30

KW - Bahadur's asymptotic efficiency

KW - Bootstrap

KW - Large deviation

KW - Moderate deviation

KW - Sample quantile

UR - http://www.scopus.com/inward/record.url?scp=85019731743&partnerID=8YFLogxK

U2 - 10.1016/j.jkss.2017.04.003

DO - 10.1016/j.jkss.2017.04.003

M3 - Article

AN - SCOPUS:85019731743

SN - 1226-3192

VL - 46

JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

IS - 4

ER -

Large and moderate deviation principles for the bootstrap sample quantile

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Keywords

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