{
  "id": "math/0604262",
  "version": "v2",
  "published": "2006-04-11T21:32:22.000Z",
  "updated": "2008-06-13T05:52:02.000Z",
  "title": "The LIL for canonical $U$-statistics",
  "authors": [
    "Radosław Adamczak",
    "Rafał Latała"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AOP351 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2008, Vol. 36, No. 3, 1023-1058",
  "doi": "10.1214/07-AOP351",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical $U$-statistics of arbitrary order $d$, extending the previously known results for $d=2$. The nasc's are expressed as growth conditions on a parameterized family of norms associated with the $U$-statistics kernel.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-13T05:52:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15"
    ],
    "keywords": [
      "sufficient conditions",
      "arbitrary order",
      "growth conditions",
      "statistics kernel"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4262A"
    }
  }
}