Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics

• 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 STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 899-917
• 关键词: edgeworth expansion; symmetrical statistics; U-statistics; jackknife; bootstrap; variance; replacement; assumptions

摘要

We study orthogonal decomposition of symmetric statistics based on samples drawn without replacement from finite populations. Several applications to finite population statistics are given: we establish one-term Edgeworth expansions for general asymptotically normal symmetric statistics, prove an Efron-Stein inequality and the consistency of the jackknife estimator of variance. Our expansions provide second order a.s. approximations to Wu's jackknife histogram.