{
  "id": "1302.1699",
  "version": "v1",
  "published": "2013-02-07T10:33:00.000Z",
  "updated": "2013-02-07T10:33:00.000Z",
  "title": "Sharp deviation bounds for quadratic forms",
  "authors": [
    "Vladimir Spokoiny"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \\(\\xiv\\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The results are stated under general conditions and do not suppose any special structure of the vector \\(\\xiv\\). The obtained bounds are exact (non-asymptotic), all constants are explicit and the leading terms in the bounds are sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-07T10:33:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "62F10"
    ],
    "keywords": [
      "sharp deviation bounds",
      "gaussian random vector",
      "finite exponential moments",
      "general quadratic form",
      "special structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1699S"
    }
  }
}