{
  "id": "1006.0502",
  "version": "v1",
  "published": "2010-06-02T21:22:33.000Z",
  "updated": "2010-06-02T21:22:33.000Z",
  "title": "Schur^2-concavity properties of Gaussian measures, with applications to hypotheses testing",
  "authors": [
    "Iosif Pinelis"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The main results imply that the probability P(\\ZZ\\in A+\\th) is Schur-concave/Schur-convex in (\\th_1^2,\\dots,\\th_k^2) provided that the indicator function of a set A in \\R^k is so, respectively; here, \\th=(\\th_1,\\dots,\\th_k) in \\R^k and \\ZZ is a standard normal random vector in \\R^k. Moreover, it is shown that the Schur-concavity/Schur-convexity is strict unless the set A is equivalent to a spherically symmetric set. Applications to testing hypotheses on multivariate means are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-02T21:22:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "62H15",
      "62F05",
      "62G20",
      "60D05",
      "62E15",
      "62E20",
      "60D05",
      "51F15",
      "53C65"
    ],
    "keywords": [
      "gaussian measures",
      "hypotheses testing",
      "applications",
      "properties",
      "standard normal random vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0502P"
    }
  }
}