EXCHANGEABLY WEIGHTED BOOTSTRAPS OF THE GENERAL EMPIRICAL PROCESS

• 成果类型: Article
• 署名作者: PRAESTGAARD, J; WELLNER, JA
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989011
• 发表日期: 1993
• 页码: 2053-2086
• 关键词: central limit-theorem; bayesian bootstrap; sample

摘要

We consider an exchangeably weighted bootstrap of the general function-indexed empirical process. We find sufficient conditions on the bootstrap weights for the central limit theorem to hold for the bootstrapped empirical process, almost surely and in probability. The results resemble those of Gine and Zinn for Efron's bootstrap. As a corollary we obtain a result on the almost sure convergence in distribution of the Efron-bootstrapped empirical process with arbitrary sample size. A large number of bootstrap resampling schemes emerge as special cases of our results.