Open Access
February 1999 Theoretical comparisons of block bootstrap methods
S. N. Lahiri
Ann. Statist. 27(1): 386-404 (February 1999). DOI: 10.1214/aos/1018031117

Abstract

In this paper, we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths. It is shown that, asymptotically, bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order. However, the variances of these bootstrap estimators may be different even in the first order. Expansions for the bias, the variance and the mean-squared error of different block bootstrap variance estimators are obtained. It follows from these expansions that using overlapping blocks is to be preferred over nonoverlapping blocks and that using random block lengths typically leads to mean-squared errors larger than those for nonrandom block lengths.

Citation

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S. N. Lahiri. "Theoretical comparisons of block bootstrap methods." Ann. Statist. 27 (1) 386 - 404, February 1999. https://doi.org/10.1214/aos/1018031117

Information

Published: February 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0945.62049
MathSciNet: MR1701117
Digital Object Identifier: 10.1214/aos/1018031117

Subjects:
Primary: 62G05
Secondary: 62E05

Keywords: block bootstrap , mean squared error , stationary bootstrap

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 1 • February 1999
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