Statistics and Computing

, Volume 22, Issue 2, pp 661–675 | Cite as

A semiparametric Bayesian approach to extreme value estimation

  • Fernando Ferraz do Nascimento
  • Dani Gamerman
  • Hedibert Freitas Lopes


This paper is concerned with extreme value density estimation. The generalized Pareto distribution (GPD) beyond a given threshold is combined with a nonparametric estimation approach below the threshold. This semiparametric setup is shown to generalize a few existing approaches and enables density estimation over the complete sample space. Estimation is performed via the Bayesian paradigm, which helps identify model components. Estimation of all model parameters, including the threshold and higher quantiles, and prediction for future observations is provided. Simulation studies suggest a few useful guidelines to evaluate the relevance of the proposed procedures. They also provide empirical evidence about the improvement of the proposed methodology over existing approaches. Models are then applied to environmental data sets. The paper is concluded with a few directions for future work.


Bayesian GPD Higher quantiles MCMC Threshold estimation Nonparametric estimation of curves 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Fernando Ferraz do Nascimento
    • 1
  • Dani Gamerman
    • 2
  • Hedibert Freitas Lopes
    • 3
  1. 1.Departamento de Informática e EstatísticaUniversidade Federal do PiauíTeresinaBrazil
  2. 2.Instituto de MatemáticaFederal University of Rio de JaneiroRio de JaneiroBrazil
  3. 3.Booth School of BusinessThe University of ChicagoChicagoUSA

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