{
  "id": "1303.2602",
  "version": "v2",
  "published": "2013-03-11T18:03:20.000Z",
  "updated": "2014-06-05T10:29:13.000Z",
  "title": "On generalized max-linear models and their statistical interpolation",
  "authors": [
    "Michael Falk",
    "Martin Hofmann",
    "Maximilian Zott"
  ],
  "comment": "32 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We propose a way how to generate a max-stable process in $C[0,1]$ from a max-stable random vector in $\\mathbb R^d$ by generalizing the \\emph{max-linear model} established by \\citet{wansto11}. It turns out that if the random vector follows some finite dimensional distribution of some initial max-stable process, the approximating processes converge uniformly to the original process and the pointwise mean squared error can be represented in a closed form. The obtained results carry over to the case of generalized Pareto processes. The introduced method enables the reconstruction of the initial process only from a finite set of observation points and, thus, reasonable prediction of max-stable processes in space becomes possible. A possible extension to arbitrary dimension is outlined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-05T10:29:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70"
    ],
    "keywords": [
      "generalized max-linear models",
      "statistical interpolation",
      "finite dimensional distribution",
      "arbitrary dimension",
      "max-stable random vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.2602F"
    }
  }
}