{
  "id": "1108.0920",
  "version": "v4",
  "published": "2011-08-03T19:56:08.000Z",
  "updated": "2012-02-07T10:59:05.000Z",
  "title": "The multivariate Piecing-Together approach revisited",
  "authors": [
    "Stefan Aulbach",
    "Michael Falk",
    "Martin Hofmann"
  ],
  "comment": "12 pages, 1 figure. To appear in the Journal of Multivariate Analysis",
  "journal": "J. Multivariate Anal. 110 (2012) 161-170",
  "doi": "10.1016/j.jmva.2012.02.002",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A multivariate extension was established by Aulbach et al. (2012a): The upper tail of a given copula C is cut off and replaced by a multivariate GPD-copula in a continuous manner, yielding a new copula called a PT-copula. Then each margin of this PT-copula is transformed by a given univariate distribution function. This provides a multivariate distribution function with prescribed margins, whose copula is a GPD-copula that coincides in its central part with C. In addition to Aulbach et al. (2012a), we achieve in the present paper an exact representation of the PT-copula's upper tail, giving further insight into the multivariate PT approach. A variant based on the empirical copula is also added. Furthermore our findings enable us to establish a functional PT version as well.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-02-07T10:59:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G32",
      "62H99",
      "60G70"
    ],
    "keywords": [
      "multivariate piecing-together approach",
      "upper tail",
      "univariate distribution function",
      "univariate piecing-together approach",
      "continuous manner"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.0920A"
    }
  }
}