Estimation of second order parameters using probability-weighted moments

Julien Worms (1) , Rym Worms (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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 $\rho$, which will be compared to other recent estimators through some simulations. Asymptotic normality results are proved~; they are especially valid in the case $\rho=0$.

Mots clés: Extreme values. Domain of attraction. Excesses. Generalized Pareto Distribution. Probability-Weighted Moments. Second order parameter. Third order conditions; Extreme values. Domain of attraction. Excesses. Generalized Pareto Distribution. Probability-Weighted Moments. Second order parameter. Third order conditions.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Julien Worms, Rym Worms. Estimation of second order parameters using probability-weighted moments. ESAIM: Probability and Statistics, 2012, 16, pp.97-113. ⟨10.1051/ps/2010017⟩. ⟨hal-00365305v2⟩