{
  "id": "1302.0516",
  "version": "v3",
  "published": "2013-02-03T17:51:47.000Z",
  "updated": "2013-04-28T02:05:47.000Z",
  "title": "More on the nonuniform Berry--Esseen bound",
  "authors": [
    "Iosif Pinelis"
  ],
  "comment": "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",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-28T02:05:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "62E17"
    ],
    "keywords": [
      "nonuniform berry-esseen bound",
      "smoothing inequalities",
      "nagaevs classical nonuniform bound",
      "simpler proof",
      "large gap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.0516P"
    }
  }
}