THE RATE OF CONVERGENCE FOR MULTIVARIATE SAMPLING STATISTICS

被引：32
|
作者：
BOLTHAUSEN, E [1 ]
GOTZE, F [1 ]
机构：
[1] UNIV BIELEFELD,FAK MATH,W-4800 BIELEFELD 1,GERMANY
来源：
ANNALS OF STATISTICS | 1993年 / 21卷 / 04期
关键词：
BERRY-ESSEEN THEOREM; MULTIVARIATE CENTRAL LIMIT THEOREM; RANK STATISTICS; SAMPLING STATISTICS;
D O I：
10.1214/aos/1176349393
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：
A Berry-Esseen theorem for the rate of convergence of general nonlinear multivariate sampling statistics with normal limit distribution is derived via a multivariate extension of Stein's method. The result generalizes in particular Previous results of Bolthausen for one-dimensional linear rank statistics, one-dimensional results of van Zwet and Friedrich for general functions of independent random elements and provides convergence bounds for general multivariate sampling statistics without restrictions on the sampling proportions.
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页码：1692 / 1710
页数：19
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