International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1951-1967

On the constant in the nonuniform version of the Berry-Esseen theorem

K. Neammanee

Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

Received 24 November 2004; Revised 8 March 2005

Copyright © 2005 K. Neammanee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In 2001, Chen and Shao gave the nonuniform estimation of the rate of convergence in Berry-Esseen theorem for independent random variables via Stein-Chen-Shao method. The aim of this paper is to obtain a constant in Chen-Shao theorem, where the random variables are not necessarily identically distributed and the existence of their third moments are not assumed. The bound is given in terms of truncated moments and the constant obtained is 21.44 for most values. We use a technique called Stein's method, in particular the Chen-Shao concentration inequality.