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February 2009 A note on the stationary bootstrap’s variance
Daniel J. Nordman
Ann. Statist. 37(1): 359-370 (February 2009). DOI: 10.1214/07-AOS567


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. "A note on the stationary bootstrap’s variance." Ann. Statist. 37 (1) 359 - 370, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62030
MathSciNet: MR2488355
Digital Object Identifier: 10.1214/07-AOS567

Primary: 62G05
Secondary: 62E05

Keywords: asymptotic expansion , block bootstrap , periodogram , spectral estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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