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January 1996 Optimal rates of convergence in the CLT for quadratic forms
V. Bentkus, F. Götze
Ann. Probab. 24(1): 466-490 (January 1996). DOI: 10.1214/aop/1042644727

Abstract

We prove optimal convergence rates in the central limit theorem for sums ${\bf R}^k.$ Assuming a fourth moment, we obtain a Berry-Esseen type bound of $O(N^{-1})$ for the probability of hitting a ball provided that $k\leq 5$. The proof still requires a technical assumption related to the independence of coordinate sums.

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V. Bentkus. F. Götze. "Optimal rates of convergence in the CLT for quadratic forms." Ann. Probab. 24 (1) 466 - 490, January 1996. https://doi.org/10.1214/aop/1042644727

Information

Published: January 1996
First available in Project Euclid: 15 January 2003

zbMATH: 0858.62010
MathSciNet: MR1387646
Digital Object Identifier: 10.1214/aop/1042644727

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 1 • January 1996
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