The Annals of Probability

On the Rate of Convergence in the Multivariate CLT

F. Gotze

Full-text: Open access

Abstract

Berry-Esseen theorems are proved in the multidimensional central limit theorem without using Fourier methods. An effective and simple estimate of the error in the CLT for sums and convex sets using Stein's method and induction is derived. Furthermore, the error in the CLT for multivariate functions of independent random elements is estimated extending results of van Zwet and Friedrich to the multivariate case.

Article information

Source
Ann. Probab. Volume 19, Number 2 (1991), 724-739.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176990448

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176990448

Mathematical Reviews number (MathSciNet)
MR1106283

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62H10: Distribution of statistics

Keywords
Central limit theorem Berry-Esseen theorem Stein's method multivariate statistics

Citation

Gotze, F. On the Rate of Convergence in the Multivariate CLT. Ann. Probab. 19 (1991), no. 2, 724--739. doi:10.1214/aop/1176990448. http://projecteuclid.org/euclid.aop/1176990448.


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