An Edgeworth expansion for symmetric statistics

被引：1

作者：

Bentkus, V

Götze, F

van Zwet, WR

机构：

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld 1, Germany

[2] Leiden Univ, Dept Math, NL-2300 RA Leiden, Netherlands

[3] Univ N Carolina, Chapel Hill, NC 27599 USA

来源：

ANNALS OF STATISTICS | 1997年 / 25卷 / 02期

关键词：

asymptotic expansion; Edgeworth expansions; symmetric statistics; Hoeffding's decomposition; U-statistics; functions of sample means; functionals of empirical distribution functions; linear combinations of order statistics; Student's statistic;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：851 / 896

页数：46

共 35 条

[21] APPROXIMATIONS FOR MULTIVARIATE U-STATISTICS [J].