International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1951-1967
doi:10.1155/IJMMS.2005.1951
On the constant in the nonuniform version of the Berry-Esseen theorem
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.
Abstract
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.