Lyapunov-type bounds for U-statistics

被引：5

作者：

Alberink, IB

Bentkus, V

机构：

[1] Univ Nijmegen, Dept Math, NL-6500 GL Nijmegen, Netherlands

[2] Inst Math & Informat, LT-2600 Vilnius, Lithuania

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2001年 / 46卷 / 04期

关键词：

U-statistics; Lyapunov-type bound; Berry-Esseen bound; rate of convergence; normal approximations;

D O I：

10.1137/S0040585X97979299

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：

Let X-1,..., X-n be independent identically distributed random variables. An optimal Lyapunov (or Berry-Esseen) bound is derived for U-statistics of degree 2, that is, statistics of the form Sigma(j<k) H(X-j, X-k), where H is a measurable, symmetric function such that E\H(X-1, X-2)\ < infinity, assuming that the statistic is nondegenerate.

引用

页码：571 / 588

页数：18

共 25 条

[1] A Berry-Esseen bound for U-statistics in the non-IID case [J].