The Annals of Probability

Optimal rates of convergence in the CLT for quadratic forms

V. Bentkus and F. Götze

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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.

Article information

Source
Ann. Probab., Volume 24, Number 1 (1996), 466-490.

Dates
First available in Project Euclid: 15 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1042644727

Digital Object Identifier
doi:10.1214/aop/1042644727

Mathematical Reviews number (MathSciNet)
MR1387646

Zentralblatt MATH identifier
0858.62010

Citation

Bentkus, V.; Götze, F. Optimal rates of convergence in the CLT for quadratic forms. Ann. Probab. 24 (1996), no. 1, 466--490. doi:10.1214/aop/1042644727. https://projecteuclid.org/euclid.aop/1042644727


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