{
  "id": "1608.02091",
  "version": "v1",
  "published": "2016-08-06T10:25:19.000Z",
  "updated": "2016-08-06T10:25:19.000Z",
  "title": "Second-order asymptotics on distributions of maxima of bivariate elliptical arrays",
  "authors": [
    "Xin Liao",
    "Zhichao Weng",
    "Zuoxiang Peng"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\{ (\\xi_{ni}, \\eta_{ni}), 1\\leq i \\leq n, n\\geq 1 \\}$ be a triangular array of independent bivariate elliptical random vectors with the same distribution function as $(S_{1}, \\rho_{n}S_{1}+\\sqrt{1-\\rho_{n}^2}S_{2})$, $\\rho_{n}\\in (0,1)$, where $(S_{1},S_{2})$ is a bivariate spherical random vector. For the distribution function of radius $\\sqrt{S_{1}^2+S_{2}^2}$ belonging to the max-domain of attraction of the Weibull distribution, Hashorva (2006) derived the limiting distribution of maximum of this triangular array if convergence rate of $\\rho_{n}$ to $1$ is given. In this paper, under the refinement of the rate of convergence of $\\rho_{n}$ to $1$ and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-06T10:25:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62E20",
      "60G70",
      "60F15",
      "60F05"
    ],
    "keywords": [
      "bivariate elliptical arrays",
      "second-order asymptotics",
      "independent bivariate elliptical random vectors",
      "distribution function",
      "precise second-order distributional expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}