Minimum Distance Estimation for the Generalized Pareto Distribution.

The generalized Pareto distribution (GPD) is widely used for extreme values over a threshold. Most existing methods for parameter estimation either perform unsatisfactorily when the shape parameterkis larger than 0.5, or they suffer from heavy computation as the sample size increases. In view of the fact thatk> 0.5 is occasionally seen in numerous applications, including two illustrative examples used in this study, we remedy the deficiencies of existing methods by proposing two new estimators for the GPD parameters. The new estimators are inspired by the minimum distance estimation and theM-estimation in the linear regression. Through comprehensive simulation, the estimators are shown to perform well for all values ofkunder small and moderate sample sizes. They are comparable to the existing methods fork< 0.5 while perform much better fork> 0.5. [ABSTRACT FROM AUTHOR]