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October, 1975 A Nonuniform Bound on Convergence to Normality
C. C. Heyde
Ann. Probab. 3(5): 903-907 (October, 1975). DOI: 10.1214/aop/1176996280

Abstract

Various asymptotically correct bounds on the uniform metric for distance between distribution functions in the central limit theorem for sums of independent and identically distributed random variables have previously been given. It is shown in the present paper that corresponding nonuniform bounds can be given for the difference between distribution functions. These results have much wider applicability, such as for obtaining probabilities of moderate deviation or for dealing with $L_p$ metrics, $1 \leqq p \leqq \infty$.

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C. C. Heyde. "A Nonuniform Bound on Convergence to Normality." Ann. Probab. 3 (5) 903 - 907, October, 1975. https://doi.org/10.1214/aop/1176996280

Information

Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0323.60021
MathSciNet: MR402861
Digital Object Identifier: 10.1214/aop/1176996280

Subjects:
Primary: 60F05
Secondary: 60F10 , 60G50

Keywords: $L_p$ metrics , central limit theorem , Convergence rates , Independent random variables , nonuniform convergence , probabilities of moderate deviations

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • October, 1975
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