Empirical Edgeworth expansions for symmetric statistics

• 成果类型: Article
• 署名作者: Putter, H; van Zwet, WR
• 署名单位: University of Amsterdam; Academic Medical Center Amsterdam; Leiden University - Excl LUMC; Leiden University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1540-1569
• 关键词: Approximation

摘要

In this paper the validity of a one-term Edgeworth expansion for Studentized symmetric statistics is proved. We propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency. As a result we obtain the second-order correctness of the empirical Edgeworth expansion for a very general class of statistics, including U-statistics, L-statistics and smooth functions of the sample mean. We illustrate the application of the bootstrap in the case of a U-statistic of degree two.