{
  "id": "math/0405342",
  "version": "v1",
  "published": "2004-05-18T02:21:35.000Z",
  "updated": "2004-05-18T02:21:35.000Z",
  "title": "Some extensions of an inequality of Vapnik and Chervonenkis",
  "authors": [
    "Dmitry Panchenko"
  ],
  "comment": "12 pages",
  "journal": "2002 Elect. Comm. in Probab. 7 55-65",
  "categories": [
    "math.PR"
  ],
  "abstract": "The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size of the expectation. Using Talagrand's kernel method we prove a similar result for the classes of functions for which Dudley's uniform entropy integral or bracketing entropy integral is finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-18T02:21:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G20"
    ],
    "keywords": [
      "inequality",
      "extensions",
      "dudleys uniform entropy integral",
      "talagrands kernel method",
      "expectation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5342P"
    }
  }
}