A semiparametric Bayesian approach to extreme value estimation
- 422 Downloads
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.
KeywordsBayesian GPD Higher quantiles MCMC Threshold estimation Nonparametric estimation of curves
Unable to display preview. Download preview PDF.
- Cabras, S., Castellanos, M.A., Gamerman, D.: A default Bayesian approach for regression on extremes. Stat. Model. (2011, accepted) Google Scholar
- Coles, S.G.: Extreme Value Theory an Applications. Kluver Academic, Dordrecht (2001) Google Scholar
- Doornik, JA: Ox: Object Oriented Matrix Programming, 4.1 console version. Nuffield College, Oxford University, London (1996) Google Scholar
- Lopes, H.F., Nascimento, F.F., Gamerman, D.: Generalized Pareto models with time-varying tail behavior. Technical Report LES:UFRJ, in preparation (2011) Google Scholar
- von Mises, R.: La distribution de la plus grande de nvaleurs. Am. Math. Soc. 2, 271–294 (1954) Google Scholar
- Nascimento, F.F., Gamerman, D., Lopes, H.F.: Regression models for exceedance data via the full likelihood. Environ. Ecol. Stat. (2011, to appear) Google Scholar
- Smith, R.L.: Threshold models for sample extremes. Statistical extremes and applications 621–638 (1984) Google Scholar