The Annals of Probability

On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem

Peter Hall

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Abstract

It is shown that "studentizing," i.e., normalizing by the sample standard deviation rather than the population standard deviation, can improve the rate of convergence in the central limit theorem. This provides concise confirmation of one feature of the folklore that a studentized sum is in some sense more robust than a normed sum. The case of infinite population standard deviation is also examined.

Article information

Source
Ann. Probab., Volume 16, Number 3 (1988), 1265-1280.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991689

Digital Object Identifier
doi:10.1214/aop/1176991689

Mathematical Reviews number (MathSciNet)
MR942767

Zentralblatt MATH identifier
0687.60021

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 rate of convergence sample variance studentizing

Citation

Hall, Peter. On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem. Ann. Probab. 16 (1988), no. 3, 1265--1280. doi:10.1214/aop/1176991689. https://projecteuclid.org/euclid.aop/1176991689


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