Open Access
June 2013 Fixed-smoothing asymptotics for time series
Xianyang Zhang, Xiaofeng Shao
Ann. Statist. 41(3): 1329-1349 (June 2013). DOI: 10.1214/13-AOS1113


In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based $t$-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location model.


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Xianyang Zhang. Xiaofeng Shao. "Fixed-smoothing asymptotics for time series." Ann. Statist. 41 (3) 1329 - 1349, June 2013.


Published: June 2013
First available in Project Euclid: 4 July 2013

zbMATH: 1273.62231
MathSciNet: MR3113813
Digital Object Identifier: 10.1214/13-AOS1113

Primary: 62G20

Keywords: bootstrap , fixed-smoothing asymptotics , high-order expansion , long-run variance matrix

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 3 • June 2013
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