Modeling extreme events: sample fraction adaptive choice in parameter estimation

M. Manuela Neves, M. Ivette Gomes, Fernanda Figueiredo, Dora Prata Gomes

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

When modeling extreme events, there are a few primordial parameters, among which we refer to the extreme value index (EVI) and the extremal index (EI). Under a framework related to large values, the EVI measures the right tail weight of the underlying distribution and the EI characterizes the degree of local dependence in the extremes of a stationary sequence. Most of the semiparametric estimators of these parameters show the same type of behavior: nice asymptotic properties but a high variance for small values of k, the number of upper order statistics used in the estimation, and a high bias for large values of k. This brings a real need for the choice of k. Choosing some well-known estimators of those two parameters, we revisit the application of a heuristic algorithm for the adaptive choice of k. A simulation study illustrates the performance of the proposed algorithm.

Original languageEnglish
Pages (from-to)184-199
Number of pages16
JournalJournal of Statistical Theory and Practice
Volume9
Issue number1(SI)
DOIs
Publication statusPublished - 13 Jan 2015

Keywords

  • Adaptive choice
  • Extremal index
  • Extreme value index
  • Sample fraction
  • Semiparametric estimation

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