Quasi-Conjugate Bayes Estimates for GPD Parameters and Application to Heavy Tails Modelling

By Jean Diebolt, Mhamed-Ali El-Aroui, M. Garrido, Stéphane Girard. 2005

60 citations recorded by the source corpus.

We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma distributions is transfered to GPD. Posterior estimates are then computed by Gibbs samplers with Hastings-Metropolis steps. Accurate Bayes credibility intervals are also defined, they provide assessment of the quality of the extreme events estimates. An empirical Bayesian method is used in this work, but the suggested approach could incorporate prior information. It is shown that the obtained quasi-conjugate Bayes estimators compare well with the GPD standard estimators when simulated and real data sets are studied.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/be9f7cb09d4a5da715e8479c97babba1b7501f68

Citations in the corpus

• Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data (2006, unknown): “Among them, Bayesian analysis recently received attention, thanks to advances in computational and numerical tools (Coles and Powell 1996; Coles and Tawn 1996; Coles and Pericchi 2003; Coles et al. 2003; Diebolt et al. 2003; Parent and Bernier 2003).”