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June, 1973 On an $L_p$ Version of the Berry-Esseen Theorem for Independent and $m$- Dependent Variables
R. V. Erickson
Ann. Probab. 1(3): 497-503 (June, 1973). DOI: 10.1214/aop/1176996944

Abstract

We show that the $L_1$ norm of the difference between the standard normal distribution and the distribution of the standardized sum of $n$ independent random variables is less than 72 $R_n$, where $R_n$ is a sum of standardized "inside" third and "outside" second moments. We conjecture that 72 can be replaced by 36 or even less. We also prove a similar result for $m$-dependent random variables, but no constant is specified.

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R. V. Erickson. "On an $L_p$ Version of the Berry-Esseen Theorem for Independent and $m$- Dependent Variables." Ann. Probab. 1 (3) 497 - 503, June, 1973. https://doi.org/10.1214/aop/1176996944

Information

Published: June, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0292.60040
MathSciNet: MR383502
Digital Object Identifier: 10.1214/aop/1176996944

Subjects:
Primary: 60F05
Secondary: 60F99

Keywords: $L_p$ Berry-Esseen , $m$-dependent , asymptotic normality and error bounds

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 3 • June, 1973
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