{
  "id": "math/0605340",
  "version": "v1",
  "published": "2006-05-12T15:26:19.000Z",
  "updated": "2006-05-12T15:26:19.000Z",
  "title": "Toward the best constant factor for the Rademacher-Gaussian tail comparison",
  "authors": [
    "Iosif Pinelis"
  ],
  "comment": "16 pages, 1 figure",
  "journal": "ESAIM Probab. Stat. 11 (2007), 412--426",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let S_n:=a_1\\vp_1+...+a_n\\vp_n, where \\vp_1,...,\\vp_n are independent Rademacher random variables (r.v.'s) and a_1,...,a_n are any real numbers such that a_1^2+...+a_n^2=1. Let Z be a standard normal r.v. It is proved that the best constant factor c in inequality \\P(S_n>x) \\leq c\\P(Z>x) for all x in \\R is between two explicitly defined absolute constants c_1 and c_2 such that c_1<c_2 \\approx 1.01c_1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-12T15:26:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "62G10",
      "62G15",
      "60G50",
      "62G35",
      "26D10"
    ],
    "keywords": [
      "best constant factor",
      "rademacher-gaussian tail comparison",
      "independent rademacher random variables",
      "explicitly defined absolute constants",
      "standard normal"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5340P"
    }
  }
}