Theoretical comparisons of block bootstrap methods

• 成果类型: Article
• 署名作者: Lahiri, SN
• 署名单位: Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1018031117
• 发表日期: 1999
• 页码: 386-404
• 关键词: stationary observations; Edgeworth Expansion; SEQUENCES; validity

摘要

In this paper, we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths. It is shown that, asymptotically, bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order. However, the variances of these bootstrap estimators may he different even in the first order. Expansions for the bias, the variance and the mean-squared error of different block bootstrap variance estimators are obtained. It follows from these expansions that using overlapping blocks is to be preferred over nonoverlapping blocks and that using random block lengths typically-leads to mean-squared errors larger than those for nonrandom block lengths.