ESAIM: Probability and Statistics

Research Article

Estimation of second order parameters using probability weighted moments

Julien Wormsa1 and Rym Wormsa2

a1 Universitéde Versailles Saint-Quentin, Laboratoire de Mathématiques de Versailles (CNRS UMR 8100), UFR de Sciences, Bât. Fermat, 45 Av. des Etats-Unis, 78035 Versailles Cedex, France. worms@math.uvsq.fr

a2 Université Paris Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050), 61 Av. du Gl de Gaulle, 94010 Créteil Cedex, France; rym.worms@univ-paris12.fr

Abstract

The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter ρ, which will be compared to other recent estimators through some simulations. Asymptotic normality results are also proved. Our new estimator of ρ looks especially competitive when  |ρ|  is small.

(Received February 27 2009)

(Revised April 16 2010)

(Online publication July 3 2012)

Key Words:

  • Extreme values;
  • domain of attraction;
  • excesses;
  • generalized Pareto distribution;
  • probability-weighted moments;
  • second order parameter;
  • third order condition.

Mathematics Subject Classification:

  • 62G32;
  • 60G70
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