Minimum Distance Estimation for the Generalized Pareto Distribution. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Chen, Piao; Ye, Zhi-Sheng; Zhao, Xingqiu
• Is Part Of: Technometrics. Volume 59:Issue 4(2017)
• Page Start: 528
• Page End: 541
• Publication Date: 2017-10-02
• Subjects: Consistency -- Extreme value -- M-estimation -- Peak over threshold -- Regression; Statistical physics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; Engineering -- Statistical methods -- Periodicals; 519.5
• DOI: 10.1080/00401706.2016.1270857
• Languages: English
• ISSNs: 0040-1706

Abstract

ABSTRACT: 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 parameter k is larger than 0.5, or they suffer from heavy computation as the sample size increases. In view of the fact that k > 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 the M -estimation in the linear regression. Through comprehensive simulation, the estimators are shown to perform well for all values of k under small and moderate sample sizes. They are comparable to the existing methods for k < 0.5 while perform much better for k > 0.5.