Minimum Distance Estimation for the Generalized Pareto Distribution

Piao Chen, Zhi Sheng Ye, Xingqiu Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)528-541
Number of pages14
JournalTechnometrics
Volume59
Issue number4
DOIs
Publication statusPublished - 2 Oct 2017

Keywords

  • Consistency
  • Extreme value
  • M-estimation
  • Peak over threshold
  • Regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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