Bootstrap Methods in Statistics of Extremes

M. Ivette Gomes, Frederico Caeiro, Lígia Henriques-Rodrigues, B.g. Manjunath

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

7 Citations (Scopus)

Abstract

In this chapter we provide an overview of the bootstrap methodology together with its possible use in the reliable estimation of any parameter of extreme events. For an asymptotically consistent choice of the threshold to use in the estimation of the extreme value index (EVI),we suggest and discuss the so-called double-bootstrap algorithm, where in each run two bootstrap samples of related sizes are generated. Such a threshold is used for the adaptive estimation of a positive EVI, also called tail index, the primary parameter in statistics of extremes. Apart from the classical Hill and peaks over random threshold (PORT)-Hill EVI estimators, we consider a class of minimum-variance reduced-bias} (MVRB) EVI estimators and associated PORT-MVRB EVI estimators. The algorithm is described for the EVI estimation, but it can work similarly for the estimation of other parameters of extreme events, like a it high quantile, the probability of exceedance, or the return period of a high level.
Original languageEnglish
Title of host publicationExtreme Events in Finance
Subtitle of host publicationA Handbook of Extreme Value Theory and its Applications
EditorsFrançois Longin
PublisherJohn Wiley & Sons, Inc.
Pages117-138
Number of pages22
ISBN (Electronic)9781118650318
ISBN (Print)9781118650196
DOIs
Publication statusPublished - 22 Aug 2016

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Keywords

  • Bootstrap methodology
  • Semiparametric estimation
  • Statistics of extremes

Cite this

Gomes, M. I., Caeiro, F., Henriques-Rodrigues, L., & Manjunath, B. G. (2016). Bootstrap Methods in Statistics of Extremes. In F. Longin (Ed.), Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications (pp. 117-138). John Wiley & Sons, Inc.. https://doi.org/10.1002/9781118650318.ch6