Threshold Selection in Extreme Value Analysis

Frederico Caeiro, M. Ivette Gomes

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

16 Citations (Scopus)

Abstract

The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the extreme value index (EVI). Whenever we are interested in large values, such estimation is usually performed on the basis of the largest k + 1 order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive EVI-estimation. Such a choice can be either heuristic or based on sample paths stability or on the minimization of a mean squared error estimate
as a function of k. Some of these procedures will be reviewed. Despite of the
fact that the methods provided can be applied, with adequate modifications, to any real EVI and not only to the adaptive EVI-estimation but also to the adaptive estimation of other relevant right-tail parameters, we shall illustrate the methods essentially for the EVI and for heavy tails, i.e., for a positive EVI.
Original languageEnglish
Title of host publicationExtreme Value Modeling and Risk Analysis
Subtitle of host publicationMethods and Applications
PublisherChapman and Hall/CRC 2007
Pages69-86
ISBN (Electronic)978-1-4987-0131-0
ISBN (Print)978-1-4987-0129-7
DOIs
Publication statusPublished - 6 Jan 2016

Keywords

  • Bootstrap methodology
  • Heuristic methods
  • Optimal sample fraction
  • Sample-paths stability
  • Semi-parametric estimation
  • Statistical theory of extremes

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  • Cite this

    Caeiro, F., & Gomes, M. I. (2016). Threshold Selection in Extreme Value Analysis. In Extreme Value Modeling and Risk Analysis: Methods and Applications (pp. 69-86). Chapman and Hall/CRC 2007. https://doi.org/10.1201/b19721-5