Rates of convergence in multivariate extreme value theory

E. Omey, S. T. Rachev

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Abstract

We discuss rates of convergence for the distribution of normalized sample extremes to the appropriate limit distribution. We show that the rate of convergence depends on that of the corresponding dependence functions and that of the marginals. The univariate results are well known by now, so we restrict our attention to dependence functions (Sections 2 and 3). In the final section of the paper we obtain a Berry-Esséen type result for multivariate extremes.

Original languageEnglish
Pages (from-to)36-50
Number of pages15
JournalJournal of Multivariate Analysis
Volume38
Issue number1
DOIs
StatePublished - Jul 1991

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Keywords

  • dependence functions
  • multivariate extreme values
  • regular variation
  • uniform rates of convergence

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