More on the nonuniform Berry--Esseen bound
Probability
2013-04-30 v3
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.
Keywords
Cite
@article{arxiv.1302.0516,
title = {More on the nonuniform Berry--Esseen bound},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1302.0516},
year = {2013}
}
Comments
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