A semiparametric Bayesian approach to extreme value estimation

  • Authors:

  • Fernando Ferraz Nascimento;Dani Gamerman;Hedibert Freitas Lopes

  • Affiliations:

  • Departamento de Informática e Estatística, Universidade Federal do Piauí, Teresina, Brazil 64049-550;Instituto de Matemática, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil 21945-970;Booth School of Business, The University of Chicago, Chicago, USA 60637

  • Venue:
  • Statistics and Computing
  • Year:
  • 2012

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Abstract

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.