More on the nonuniform Berry--Esseen bound

Abstract

Certain smoothing inequalities were proposed in the recent paper posted on arXiv at arxiv:1301.2828 in order to lessen the very large gap between the best correctly established upper and lower bounds on the constant factor in the nonuniform Berry-Esseen bound. As an illustration of the possible uses of those inequalities, a quick proof of Nagaev's classical nonuniform bound was given there. Here we describe another, apparently more effective class of smoothing inequalities, and give a yet quicker and simpler proof of Nagaev's result.

Version 2: bounding of the "inconvenient" term containing |X| and discussed in Remark 3.4 is improved. Version 3: citation of http://arxiv.org/abs/1301.2828 is updated