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November, 1982 Bounds on the Rate of Convergence of Moments in the Central Limit Theorem
Peter Hall
Ann. Probab. 10(4): 1004-1018 (November, 1982). DOI: 10.1214/aop/1176993721


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.


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Peter Hall. "Bounds on the Rate of Convergence of Moments in the Central Limit Theorem." Ann. Probab. 10 (4) 1004 - 1018, November, 1982.


Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0516.60025
MathSciNet: MR672300
Digital Object Identifier: 10.1214/aop/1176993721

Primary: 60F05
Secondary: 60G50

Keywords: central limit theorem , moments , norming constants , rates of convergence

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 4 • November, 1982
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