On the blockwise bootstrap for empirical processes for stationary sequences

• 成果类型: Article
• 署名作者: Peligrad, M
• 署名单位: University System of Ohio; University of Cincinnati
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022855654
• 发表日期: 1998
• 页码: 877-901
• 关键词: central limit-theorem; mixing sequences; CONVERGENCE; jackknife

摘要

In this paper, we study the weak convergence to an appropriate Gaussian process of the empirical process of the block-based bootstrap estimator proposed by Kunsch for stationary sequences. The classes of processes investigated are weak dependent and associated sequences. We also prove that, differently from the independent situation, the bootstrapped estimator of the mean of certain dependent sequences satisfies the central limit theorem while the mean of the original sequence does not.