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Adaptive estimation of heavy right tails: resampling-based methods in action

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Abstract

In this paper, we discuss an algorithm for the adaptive estimation of a positive extreme value index, γ, the primary parameter in Statistics of Extremes. Apart from the classical extreme value index estimators, we suggest the consideration of associated second-order corrected-bias estimators, and propose the use of resampling-based computer-intensive methods for an asymptotically consistent choice of the thresholds to use in the adaptive estimation of γ. The algorithm is described for a classical γ-estimator and associated corrected-bias estimator, but it can work similarly for the estimation of other parameters of extreme events, like a high quantile, the probability of exceedance or the return period of a high level.

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Authors and Affiliations

  1. Universidade de Lisboa, FCUL, DEIO and CEAUL, Lisboa, Portugal

    M. Ivette Gomes

  2. Faculdade de Economia and CEAUL, Universidade do Porto, Porto, Portugal

    Fernanda Figueiredo

  3. Instituto Superior de Agronomia and CEAUL, Universidade Técnica de Lisboa, Lisboa, Portugal

    M. Manuela Neves

Authors
  1. M. Ivette Gomes
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  2. Fernanda Figueiredo
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  3. M. Manuela Neves
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Corresponding author

Correspondence to M. Ivette Gomes.

Additional information

Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011 and PTDC/FEDER.

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Gomes, M.I., Figueiredo, F. & Neves, M.M. Adaptive estimation of heavy right tails: resampling-based methods in action. Extremes 15, 463–489 (2012). https://doi.org/10.1007/s10687-011-0146-6

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  • DOI: https://doi.org/10.1007/s10687-011-0146-6

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