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August, 1981 $\mathrm{L}_\infty$-Bound for Asymptotic Normality of Weakly Dependent Summands Using Stein's Result
Hiroshi Takahata
Ann. Probab. 9(4): 676-683 (August, 1981). DOI: 10.1214/aop/1176994375

Abstract

Let $\{X_n\}$ be a strictly stationary process satisfying some mixing conditions, including $\phi$-mixing condition. It is the aim of the present paper to give, using a slight modification of Stein's result, a rate $O(n^{-1/2} \log n)$ of the normal approximation for a sum $S_n = X_1 + \cdots + X_n$.

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Hiroshi Takahata. "$\mathrm{L}_\infty$-Bound for Asymptotic Normality of Weakly Dependent Summands Using Stein's Result." Ann. Probab. 9 (4) 676 - 683, August, 1981. https://doi.org/10.1214/aop/1176994375

Information

Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0465.60033
MathSciNet: MR624695
Digital Object Identifier: 10.1214/aop/1176994375

Subjects:
Primary: 60F05
Secondary: 60G10

Keywords: Mixing , rate of the normal approximation , stationary process

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 4 • August, 1981
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