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

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

2006-02-15

arxiv.org/abs/math/0602328v1

Annals of Statistics 2005, Vol. 33, No. 5, 2475-2506

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000507 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000507

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.

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