FIXED-SMOOTHING ASYMPTOTICS FOR TIME SERIES

• 成果类型: Article
• 署名作者: Zhang, Xianyang; Shao, Xiaofeng
• 署名单位: University of Missouri System; University of Missouri Columbia; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1113
• 发表日期: 2013
• 页码: 1329-1349
• 关键词: consistent covariance-matrix; AUTOCORRELATION ROBUST-TESTS; autocovariance matrices; Edgeworth expansions; weak dependence; bootstrap; heteroskedasticity; estimators; eigenvalues; regression

摘要

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.