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Consistency of the jackknife-after-bootstrap variance estimator for the bootstrap quantiles of a Studentized statistic. (English) Zbl 1086.62033
Summary: B. Efron [J. R. Stat. Soc., Ser. B 54, No. 1, 83–127 (1992; Zbl 0782.62051]] 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 S. N. Lahiri [Econom. Theory 18, No. 1, 79–98 (2002; Zbl 1181.62058]). 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.

MSC:
62F12 Asymptotic properties of parametric estimators
62F40 Bootstrap, jackknife and other resampling methods
62G09 Nonparametric statistical resampling methods
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
62G20 Asymptotic properties of nonparametric inference
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