A location-invariant probability weighted moment estimation of the Extreme Value Index

Frederico Almeida Gião Gonçalves Caeiro, M. Ivette Gomes, Lígia Henriques-Rodrigues

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.

Original languageEnglish
Pages (from-to)676-695
Number of pages20
JournalInternational Journal of Computer Mathematics
Volume93
Issue number4
DOIs
Publication statusPublished - 2 Apr 2016

Keywords

  • adaptive semi-parametric estimation
  • asymptotic properties
  • bootstrap methodology
  • Extreme Value Index
  • heavy tails
  • location/scale-invariant estimation
  • Monte-Carlo simulation
  • statistics of extremes

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