Bootstrap and empirical likelihood methods in extremes

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Abstract

One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domain of attraction of an extreme-value distribution and to predict rare events. In recent years, much effort in developing new methodologies has been made by many researchers in this area so as to diminish the impact of the bias in the estimation and achieve some asymptotic optimality in inference problems such as estimating the optimal sample fractions and constructing confidence intervals of various quantities. In particular, bootstrap and empirical likelihood methods, which have been widely used in many areas of statistics, have drawn attention. This paper reviews some novel applications of the bootstrap and the empirical likelihood techniques in extreme-value statistics.

Original languageEnglish (US)
Pages (from-to)81-97
Number of pages17
JournalExtremes
Volume11
Issue number1
DOIs
StatePublished - Mar 2008

Keywords

  • Bootstrap
  • Confidence interval
  • Empirical likelihood
  • Extremes
  • High quantile
  • Sample fraction
  • Tail index

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