| Issue |
ESAIM: PS
Volume 16, 2012
|
|
|---|---|---|
| Page(s) | 97 - 113 | |
| DOI | https://doi.org/10.1051/ps/2010017 | |
| Published online | 03 July 2012 | |
Estimation of second order parameters using probability weighted moments
1 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
2 Université Paris Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050), 61 Av. du G l de Gaulle, 94010 Créteil Cedex, France
rym.worms@univ-paris12.fr
Received: 27 February 2009
Revised: 16 April 2010
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.
Mathematics Subject Classification: 62G32 / 60G70
Key words: Extreme values / domain of attraction / excesses / generalized Pareto distribution / probability-weighted moments / second order parameter / third order condition.
© EDP Sciences, SMAI, 2012
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