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

摘要

In 2001, Chen and Shao gave the nonuniform estimation of the rateof convergence in Berry-Esseen theorem for independent randomvariables via Stein-Chen-Shao method. The aim of this paper is toobtain a constant in Chen-Shao theorem, where the random variablesare not necessarily identically distributed and theexistence of their third moments are not assumed. The bound isgiven in terms of truncated moments and the constant obtained is21.44for most values. We use a technique called Stein's method,in particular the Chen-Shao concentration inequality.