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.

引用

页码：1692 / 1710

页数：19

共 8 条

[1] STEIN METHOD FOR DIFFUSION APPROXIMATIONS
BARBOUR, AD
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1990, 84 (03) : 297 - 322
[2] BOLTHAUSEN E, 1984, Z WAHRSCHEINLICHKEIT, V66, P379, DOI 10.1007/BF00533704
[3] A BERRY-ESSEEN BOUND FOR FUNCTIONS OF INDEPENDENT RANDOM-VARIABLES
FRIEDRICH, KO
[J]. ANNALS OF STATISTICS, 1989, 17 (01) : 170 - 183
[4] EDGEWORTH EXPANSIONS FOR LINEAR RANK STATISTICS
SCHNELLER, W
[J]. ANNALS OF STATISTICS, 1989, 17 (03) : 1103 - 1123
[5] STEIN C, 1972, 6TH P BERK S MATH ST, V2, P583
[6] Stein C., 1986, I MATH STAT LECT NOT, V7
[7] ON THE ASYMPTOTIC PROPERTIES OF THE JACKKNIFE HISTOGRAM
WU, CFJ
[J]. ANNALS OF STATISTICS, 1990, 18 (03) : 1438 - 1452
[8] ZHAO L, 1987, SCIENTIA SINICA A, V2, P113

← 1 →