A note on the stationary bootstrap's variance

Details A note on the stationary bootstrap's variance A note on the stationary bootstrap's variance

2009-03-03

arxiv.org/abs/0903.0474v1

Annals of Statistics 2009, Vol. 37, No. 1, 359-370

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS567 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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