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Resampling-Based Methodologies in Statistics of Extremes: Environmental and Financial Applications

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Mathematics of Energy and Climate Change

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 2))

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Abstract

Resampling computer intensive methodologies, like the jackknife and the bootstrap are important tools for a reliable semi-parametric estimation of parameters of extreme or even rare events. Among these parameters we mention the extreme value index, ξ, the primary parameter in statistics of extremes. Most of the semi-parametric estimators of this parameter show the same type of behaviour: nice asymptotic properties, but a high variance for small k, the number of upper order statistics used in the estimation, a high bias for large k, and the need for an adequate choice of k. After a brief reference to some estimators of the aforementioned parameter and their asymptotic properties we present an algorithm that deals with an adaptive reliable estimation of ξ. Applications of these methodologies to the analysis of environmental and financial data sets are undertaken.

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Acknowledgements

Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, projects PEst-OE/MAT/UI0006/2011, 2014 (CEAUL), EXTREMA, PTDC/MAT/101736/2008, and grant SFRH/BPD/77319/2011.

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Authors and Affiliations

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

    M. Ivette Gomes

  2. Universidade de São Paulo, IME, and CEAUL, São Paulo, Brasil

    Lígia Henriques-Rodrigues

  3. Universidade do Porto, FEP, and CEAUL, Porto, Portugal

    Fernanda Figueiredo

Authors
  1. M. Ivette Gomes
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  2. Lígia Henriques-Rodrigues
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  3. Fernanda Figueiredo
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Corresponding author

Correspondence to M. Ivette Gomes .

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Editors and Affiliations

  1. IHES Le Bois-Marie, Bures-sur-Yvette, France

    Jean-Pierre Bourguignon

  2. Department of Mathematics, ETH Zürich; Seminar für Angewandte Mathematik, Zürich, Switzerland

    Rolf Jeltsch

  3. Department of Mathematics, University of Porto; Faculty of Sciences, Porto, Portugal

    Alberto Adrego Pinto

  4. Instituto de Matemática Pura e Aplicada, IMPA, Rio de Janeiro, Brazil

    Marcelo Viana

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Gomes, M.I., Henriques-Rodrigues, L., Figueiredo, F. (2015). Resampling-Based Methodologies in Statistics of Extremes: Environmental and Financial Applications. In: Bourguignon, JP., Jeltsch, R., Pinto, A., Viana, M. (eds) Mathematics of Energy and Climate Change. CIM Series in Mathematical Sciences, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-16121-1_6

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