The Annals of Statistics
- Ann. Statist.
- Volume 41, Number 3 (2013), 1329-1349.
Fixed-smoothing asymptotics for time series
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.
Ann. Statist., Volume 41, Number 3 (2013), 1329-1349.
First available in Project Euclid: 4 July 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G20: Asymptotic properties
Zhang, Xianyang; Shao, Xiaofeng. Fixed-smoothing asymptotics for time series. Ann. Statist. 41 (2013), no. 3, 1329--1349. doi:10.1214/13-AOS1113. https://projecteuclid.org/euclid.aos/1372979640
- Supplementary material: Proofs of the other results in Sections 2–3 and simulation results. This supplement contains proofs of the other main results in Sections 2–3 and some simulation results.