{
  "id": "math/0503651",
  "version": "v1",
  "published": "2005-03-29T07:02:00.000Z",
  "updated": "2005-03-29T07:02:00.000Z",
  "title": "Moment inequalities for functions of independent random variables",
  "authors": [
    "Stephane Boucheron",
    "Olivier Bousquet",
    "Gabor Lugosi",
    "Pascal Massart"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000000856 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2005, Vol. 33, No. 2, 514-560",
  "doi": "10.1214/009117904000000856",
  "categories": [
    "math.PR"
  ],
  "abstract": "A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003) 1583-1614], and is based on a generalized tensorization inequality due to Latala and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147-168]. The new inequalities prove to be a versatile tool in a wide range of applications. We illustrate the power of the method by showing how it can be used to effortlessly re-derive classical inequalities including Rosenthal and Kahane-Khinchine-type inequalities for sums of independent random variables, moment inequalities for suprema of empirical processes and moment inequalities for Rademacher chaos and U-statistics. Some of these corollaries are apparently new. In particular, we generalize Talagrand's exponential inequality for Rademacher chaos of order 2 to any order. We also discuss applications for other complex functions of independent random variables, such as suprema of Boolean polynomials which include, as special cases, subgraph counting problems in random graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-29T07:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60C05",
      "28A35",
      "05C80"
    ],
    "keywords": [
      "independent random variables",
      "rademacher chaos",
      "generalize talagrands exponential inequality",
      "massart ann",
      "generalized tensorization inequality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3651B"
    }
  }
}