ON THE VALIDITY OF RESAMPLING METHODS UNDER LONG MEMORY

• 成果类型: Article
• 署名作者: Bai, Shuyang; Taqqu, Murad S.
• 署名单位: University System of Georgia; University of Georgia; Boston University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1524
• 发表日期: 2017
• 页码: 2365-2399
• 关键词: CENTRAL LIMIT-THEOREMS; sampling window method; subsampling inference; nonlinear functionals; BLOCK BOOTSTRAP; AUTOCORRELATIONS; autocovariances

摘要

For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic consistency of subsampling procedures for general statistics under long memory. It allows the subsample size b to be o(n), where n is the sample size, irrespective of the strength of the memory. We are then able to improve many results found in the literature. We also consider applications of subsampling procedures under long memory to the sample covariance, M-estimation and empirical processes.