## The Annals of Statistics

### Fixed-smoothing asymptotics for time series

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 41, Number 3 (2013), 1329-1349.

Dates
First available in Project Euclid: 4 July 2013

https://projecteuclid.org/euclid.aos/1372979640

Digital Object Identifier
doi:10.1214/13-AOS1113

Mathematical Reviews number (MathSciNet)
MR3113813

Zentralblatt MATH identifier
1273.62231

Subjects
Primary: 62G20: Asymptotic properties

#### Citation

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

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#### Supplemental materials

• 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.