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The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results to the case where parameters are estimated.
@article{PS_2003__7__219_0,
author = {Diebolt, Jean and Guillou, Armelle and Worms, Rym},
title = {Asymptotic behaviour of the probability-weighted moments and penultimate approximation},
journal = {ESAIM: Probability and Statistics},
pages = {219--238},
publisher = {EDP-Sciences},
volume = {7},
year = {2003},
doi = {10.1051/ps:2003010},
mrnumber = {1987787},
zbl = {1017.60060},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2003010/}
}
TY - JOUR AU - Diebolt, Jean AU - Guillou, Armelle AU - Worms, Rym TI - Asymptotic behaviour of the probability-weighted moments and penultimate approximation JO - ESAIM: Probability and Statistics PY - 2003 SP - 219 EP - 238 VL - 7 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2003010/ DO - 10.1051/ps:2003010 LA - en ID - PS_2003__7__219_0 ER -
%0 Journal Article %A Diebolt, Jean %A Guillou, Armelle %A Worms, Rym %T Asymptotic behaviour of the probability-weighted moments and penultimate approximation %J ESAIM: Probability and Statistics %D 2003 %P 219-238 %V 7 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2003010/ %R 10.1051/ps:2003010 %G en %F PS_2003__7__219_0
Diebolt, Jean; Guillou, Armelle; Worms, Rym. Asymptotic behaviour of the probability-weighted moments and penultimate approximation. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 219-238. doi: 10.1051/ps:2003010
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