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Estimation of second order parameters using probability weighted moments

Published online by Cambridge University Press:  03 July 2012

Julien Worms  and
Rym Worms
Julien Worms
Affiliation:
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. [email protected]
Rym Worms
Affiliation:
Université Paris Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050), 61 Av. du Gl de Gaulle, 94010 Créteil Cedex, France; [email protected]
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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.

Keywords

Extreme valuesdomain of attractionexcessesgeneralized Pareto distributionprobability-weighted momentssecond order parameterthird order condition.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012 , pp. 97 - 113
Copyright
© EDP Sciences, SMAI, 2012

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