The Annals of Statistics

The Rate of Convergence for Multivariate Sampling Statistics

Erwin Bolthausen and Friedrich Gotze

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Abstract

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.

Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 1692-1710.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349393

Digital Object Identifier
doi:10.1214/aos/1176349393

Mathematical Reviews number (MathSciNet)
MR1245764

Zentralblatt MATH identifier
0798.62023

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory

Keywords
Berry-Esseen theorem multivariate central limit theorem rank statistics sampling statistics

Citation

Bolthausen, Erwin; Gotze, Friedrich. The Rate of Convergence for Multivariate Sampling Statistics. Ann. Statist. 21 (1993), no. 4, 1692--1710. doi:10.1214/aos/1176349393. https://projecteuclid.org/euclid.aos/1176349393


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