Consistency of the jackknife-after-bootstrap variance estimator for the bootstrap quantiles of a Studentized statistic

The Annals of Statistics · 2005 · Volume 33 · Issue 5

Abstract

Efron [J. Roy. Statist. Soc. Ser. B 54 (1992) 83–111] proposed a computationally efficient method, called the jackknife-after-bootstrap, for estimating the variance of a bootstrap estimator for independent data. For dependent data, a version of the jackknife-after-bootstrap method has been recently proposed by Lahiri [Econometric Theory 18 (2002) 79–98]. In this paper it is shown that the jackknife-after-bootstrap estimators of the variance of a bootstrap quantile are consistent for both dependent and independent data. Results from a simulation study are also presented.

Keywords

62G05, 62G25, block bootstrap, consistency, jackknife, Weak dependence

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