The Annals of Probability

Characterizing the Rate of Convergence in the Central Limit Theorem

Peter Hall

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Abstract

Asymptotic upper and lower bounds are obtained for the uniform measure of the rate of convergence in the central limit theorem using a variety of norming constants. For many distributions the upper and lower bounds are of the same order of magnitude. As easy corollaries we deduce extensive generalizations of the classical characterizations of the rate of convergence in terms of series and order of magnitude conditions.

Article information

Source
Ann. Probab., Volume 8, Number 6 (1980), 1037-1048.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994566

Digital Object Identifier
doi:10.1214/aop/1176994566

Mathematical Reviews number (MathSciNet)
MR602378

Zentralblatt MATH identifier
0456.60018

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G50: Sums of independent random variables; random walks

Keywords
Rate of convergence central limit theorem independent and identically distributed random variables

Citation

Hall, Peter. Characterizing the Rate of Convergence in the Central Limit Theorem. Ann. Probab. 8 (1980), no. 6, 1037--1048. doi:10.1214/aop/1176994566. https://projecteuclid.org/euclid.aop/1176994566


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