Estimation of second order parameters using probability weighted moments
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 97-113

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.

DOI : 10.1051/ps/2010017
Classification : 62G32, 60G70
Keywords: extreme values, domain of attraction, excesses, generalized Pareto distribution, probability-weighted moments, second order parameter, third order condition 
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     author = {Worms, Julien and Worms, Rym},
     title = {Estimation of second order parameters using probability weighted moments},
     journal = {ESAIM: Probability and Statistics},
     pages = {97--113},
     year = {2012},
     publisher = {EDP Sciences},
     volume = {16},
     doi = {10.1051/ps/2010017},
     mrnumber = {2946122},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2010017/}
}
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Worms, Julien; Worms, Rym. Estimation of second order parameters using probability weighted moments. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 97-113. doi: 10.1051/ps/2010017

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