Bootstrapping the student t-statistic

• 成果类型: Article
• 署名作者: Mason, DM; Shao, QM
• 署名单位: University of Delaware; University of Oregon
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1015345757
• 发表日期: 2001
• 页码: 1435-1450
• 关键词: sample-size; arbitrary

摘要

Let X-1,..., X-n, n greater than or equal to 1, be independent, identically distributed random variables and consider the Student t-statistic T-n based upon these random variables. Gine, Gotze and Mason (1997) proved that T-n converges in distribution to a standard normal random variable if and only if X is in the domain of attraction of a normal random variable and EX = 0. We shall show that roughly the same holds true for the bootstrapped Student t-statistic T-n*. In the process we shall disclose all the possible subsequential limiting laws of T-n*. The proofs introduce a number of amusing tricks that may be of independent interest.