Journal
ANNALS OF STATISTICS
Volume 37, Issue 1, Pages 359-370Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/07-AOS567
Keywords
Asymptotic expansion; block bootstrap; periodogram; spectral estimation
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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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