An Edgeworth expansion for symmetric statistics

• 成果类型: Article
• 署名作者: Bentkus, V; Götze, F; van Zwet, WR
• 署名单位: University of Bielefeld; Leiden University; Leiden University - Excl LUMC; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 851-896
• 关键词: berry-esseen theorem; U-statistics; asymptotic expansions; CONVERGENCE

摘要

We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder O(N-1) under Cramer's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder o(N-1) without imposing additional assumptions on the structure of the nonlinear part of the statistic.