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The rate of convergence for multivariate sampling statistics


Bolthausen, E; Götze, F (1993). The rate of convergence for multivariate sampling statistics. Annals of Statistics, 21(4):1692-1710.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Berry-Esseen theorem; multivariate central limit theorem; rank statistics; sampling statistics
Language:English
Date:1993
Deposited On:20 May 2010 15:37
Last Modified:05 Apr 2016 13:28
Publisher:Institute of Mathematical Statistics
ISSN:0090-5364
Publisher DOI:https://doi.org/10.1214/aos/1176349393
Related URLs:http://www.zentralblatt-math.org/zmath/en/search/?q=an:0798.62023

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