Iosif Pinelis
Published 2013-02-03, updated 2013-04-28Version 3
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.
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
On the nonuniform Berry--Esseen bound
Nonuniform Berry-Esseen bound for self-normalized martingales
A simpler proof of the negative association property for absolute values of measures tied to generalized Orlicz balls
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