A Berry-Esseen bound for U-statistics in the non-IID case

被引：10
|
作者：
Alberink, IB [1 ]
机构：
[1] Univ Nijmegen, Dept Math, NL-6500 GL Nijmegen, Netherlands
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2000年 / 13卷 / 02期
关键词：
U-statistics; Berry Esseen bound; non-i.i.d sampling; rate of convergence; Wilcoxon's rank-sum test;
D O I：
10.1023/A:1007889323347
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, not necessarily identically distributed random variables. An optimal Berry Esseen bound is derived for U-statistics of order 2, that is, statistics of the form T = Sigma(1 less than or equal to i<j less than or equal to n) g(ij) (X-i, X-j), where the g(ij) are measurable functions such that if E \g(j)(X-i, X-j)\ < infinity. An application is given concerning Wilcoxon's rank-sum test.
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页码：519 / 533
页数：15
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