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June, 1974 $L_1$ Bounds for Asymptotic Normality of $m$-Dependent Sums Using Stein's Technique
R. V. Erickson
Ann. Probab. 2(3): 522-529 (June, 1974). DOI: 10.1214/aop/1176996670

Abstract

In a recent paper, C. Stein has given a new, direct technique for bounding the error of the normal approximation to the distribution of a sum of dependent random variables, assuming the variables form a stationary sequence with eighth moments. In the present paper we give two $L_1$ bounds on this error for an arbitrary $m$-dependent sequence with second moments.

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R. V. Erickson. "$L_1$ Bounds for Asymptotic Normality of $m$-Dependent Sums Using Stein's Technique." Ann. Probab. 2 (3) 522 - 529, June, 1974. https://doi.org/10.1214/aop/1176996670

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0301.60020
MathSciNet: MR383503
Digital Object Identifier: 10.1214/aop/1176996670

Subjects:
Primary: 60F05
Secondary: 60F99

Keywords: $L_1$ Berry-Esseen , $m$-dependent , asymptotic normality and error bounds

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • June, 1974
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