{
  "id": "1111.3486",
  "version": "v2",
  "published": "2011-11-15T10:15:41.000Z",
  "updated": "2014-10-22T11:53:35.000Z",
  "title": "New concentration inequalities for suprema of empirical processes",
  "authors": [
    "Johannes C. Lederer",
    "Sara A. van de Geer"
  ],
  "comment": "Published in at http://dx.doi.org/10.3150/13-BEJ549 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2014, Vol. 20, No. 4, 2020-2038",
  "doi": "10.3150/13-BEJ549",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive concentration inequalities assuming only low moments for an envelope of the empirical process. These concentration inequalities are beneficial even when the envelope is much larger than the single functions under consideration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-15T10:15:41.000Z",
      "title": "New Concentration Inequalities for Suprema of Empirical Processes",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-22T11:53:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "empirical processes",
      "strict tail assumptions",
      "effective concentration inequalities",
      "low moments",
      "considerably weaker assumptions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3486L"
    }
  }
}