On Pickands coordinates in arbitrary dimensions

  • Authors:

  • Michael Falk;Rolf-Dieter Reiss

  • Affiliations:

  • Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany;Fachbereich Mathematik, Universität Siegen, D-57068 Siegen, Germany

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2005

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Abstract

Pickands coordinates were introduced as a crucial tool for the investigation of bivariate extreme value models. We extend their definition to arbitrary dimensions and, thus, we can generalize many known results for bivariate extreme value and generalized Pareto models to higher dimensions and arbitrary extreme value margins.In particular we characterize multivariate generalized Pareto distributions (GPs) and spectral δ-neighborhoods of GPs in terms of best attainable rates of convergence of extremes, which are well-known results in the univariate case. A sufficient univariate condition for a multivariate distribution function (df) to belong to the domain of attraction of an extreme value df is derived. Bounds for the variational distance in peaks--over threshold models are established, which are based on Pickands coordinates.