{
  "id": "0704.1643",
  "version": "v1",
  "published": "2007-04-12T19:27:46.000Z",
  "updated": "2007-04-12T19:27:46.000Z",
  "title": "The LIL for $U$-statistics in Hilbert spaces",
  "authors": [
    "Radosław Adamczak",
    "Rafał Latała"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, which are of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-12T19:27:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60E15"
    ],
    "keywords": [
      "hilbert spaces",
      "statistics",
      "sufficient conditions",
      "tail estimates",
      "arbitrary order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.1643A"
    }
  }
}