The Annals of Statistics

Theoretical comparisons of block bootstrap methods

S. N. Lahiri

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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.

Article information

Ann. Statist., Volume 27, Number 1 (1999), 386-404.

First available in Project Euclid: 5 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62E05

Block bootstrap mean squared error stationary bootstrap


Lahiri, S. N. Theoretical comparisons of block bootstrap methods. Ann. Statist. 27 (1999), no. 1, 386--404. doi:10.1214/aos/1018031117.

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