A New Hybrid Estimation Method for the Generalized Pareto Distribution

• Activity Number: 317
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: SSC
• Author(s): Chunlin Wang*+ and Gemai Chen
• Companies: University of Waterloo and University of Calgary
• Keywords: extreme values ; maximum goodness-of-fit estimator ; maximum likelihood estimator ; minimum distance estimator ; parameter profiling

Abstract

The generalized Pareto distribution (GPD) is important in the analysis of extreme values, especially in modeling the exceedances over thresholds. Most of the existing methods for estimating the scale and shape parameters $\sigma$ and $k$ of the GPD suffer from theoretical and/or computational problems. To improve the existing methods in terms of bias and mean squared error, and to simplify the computation, a new hybrid estimation method is proposed, which minimizes a goodness-of-fit measure and incorporates some useful likelihood information. Compared with the maximum likelihood estimators and the maximum goodness-of-fit estimators, our new hybrid estimators can not only reduce the estimation bias but also improve the mean squared error. Our hybrid estimators also perform better compared with other estimators over several parameter regions, including those suggested in the most recent literature. The new method will be illustrated through a sea waves data set.