A Bayesian semi-parametric approach to extreme regime identification

Abstract

The limiting tail behaviour of distributions is known to follow one of three possible limiting distributions, depending on the domain of attraction of the observational model under suitable regularity conditions. This work proposes a new approach for identification and analysis of the shape parameter of the GPD as a mixture distribution over the three possible regimes. This estimation is based on evaluation of posterior probabilities for each regime. The model-based approach uses a mixture at the observational level where a Generalized Pareto distribution (GPD) is assumed above the threshold, and mixture of Gammas distributions is used under a threshold. The threshold is also estimated. Simulation exercises were conducted to evaluate the accuracy of the model for various parameter settings and sample sizes, specifically in the estimation of high quantiles. They show an improved performance over existing approaches. The paper also compares inferences based on Bayesian regime choice against Bayesian averaging over the regimes. Results of environmental applications show the correctly identifying the GPD regime plays a vital role in these studies.