{
  "id": "math/0503660",
  "version": "v1",
  "published": "2005-03-29T08:41:32.000Z",
  "updated": "2005-03-29T08:41:32.000Z",
  "title": "Sectorial convergence of U-statistics",
  "authors": [
    "Anda Gadidov"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000001080 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, 816-822",
  "doi": "10.1214/009117904000001080",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in Z^d_+ is equivalent to convergence along the diagonal of Z^d_+, as it is considered in Lata\\la and Zinn [Ann. Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums of multi-indexed i.i.d. random variables are also made.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-29T08:41:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60E15"
    ],
    "keywords": [
      "sectorial convergence",
      "sure convergence",
      "linear sector",
      "similar results",
      "random variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3660G"
    }
  }
}