The Annals of Probability

Bounds on the Rate of Convergence of Moments in the Central Limit Theorem

Peter Hall

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Abstract

We derive two-sided bounds on the rate of convergence of moments in the central limit theorem. A variety of norming constants is considered, and it is shown that a very delicate alteration to these constants can have a significant effect on the rate. Indeed, the influence of norming constants on rates of convergence of moments is of a more subtle nature than in the central limit theorem itself. We present several examples to illustrate some extreme cases.

Article information

Source
Ann. Probab., Volume 10, Number 4 (1982), 1004-1018.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993721

Digital Object Identifier
doi:10.1214/aop/1176993721

Mathematical Reviews number (MathSciNet)
MR672300

Zentralblatt MATH identifier
0516.60025

JSTOR
links.jstor.org

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

Keywords
Central limit theorem moments norming constants rates of convergence

Citation

Hall, Peter. Bounds on the Rate of Convergence of Moments in the Central Limit Theorem. Ann. Probab. 10 (1982), no. 4, 1004--1018. doi:10.1214/aop/1176993721. https://projecteuclid.org/euclid.aop/1176993721


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