An Edgeworth expansion for symmetric finite population statistics

• 成果类型: Article
• 署名作者: Bloznelis, M; Götze, F
• 署名单位: Vilnius University; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 1238-1265
• 关键词: distribution-free tests; berry-esseen bounds; asymptotic expansions; U-statistics; replacement; bootstrap; samples; POWER

摘要

Let T be a symmetric statistic based on sample of size n drawn without replacement from a finite population of size N, where N > n. Assuming that the linear part of Hoeffding's decomposition of T is nondegenerate we construct a one term Edgeworth expansion for the distribution function of T and prove the validity of the expansion with the remainder O(1/n*) as n* --> infinity, where n* = min{n, N - n}.