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arXiv · 0903.0474

A note on the stationary bootstrap's variance

Daniel J. Nordman
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Abstract

Because the stationary bootstrap resamples data blocks of random length, this method has been thought to have the largest asymptotic variance among block bootstraps Lahiri [Ann. Statist. 27 (1999) 386--404]. It is shown here that the variance of the stationary bootstrap surprisingly matches that of a block bootstrap based on nonrandom, nonoverlapping blocks. This argument translates the variance expansion into the frequency domain and provides a unified way of determining variances for other block bootstraps. Some previous results on the stationary bootstrap, related to asymptotic relative efficiency and optimal block size, are also updated.

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Daniel J. Nordman. 2009-03-03. A note on the stationary bootstrap's variance. https://doi.org/10.1214/07-aos567

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