Estimation of second order parameters using probability weighted moments

Julien Worms; Rym Worms

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 97-113
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Worms, Julien, and Worms, Rym. "Estimation of second order parameters using probability weighted moments." ESAIM: Probability and Statistics 16 (2012): 97-113. <http://eudml.org/doc/273613>.

@article{Worms2012,
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.},
author = {Worms, Julien, Worms, Rym},
journal = {ESAIM: Probability and Statistics},
keywords = {extreme values; domain of attraction; excesses; generalized Pareto distribution; probability-weighted moments; second order parameter; third order condition; second-order parameter; third-order condition},
language = {eng},
pages = {97-113},
publisher = {EDP-Sciences},
title = {Estimation of second order parameters using probability weighted moments},
url = {http://eudml.org/doc/273613},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Worms, Julien
AU - Worms, Rym
TI - Estimation of second order parameters using probability weighted moments
JO - ESAIM: Probability and Statistics
PY - 2012
PB - EDP-Sciences
VL - 16
SP - 97
EP - 113
AB - 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.
LA - eng
KW - extreme values; domain of attraction; excesses; generalized Pareto distribution; probability-weighted moments; second order parameter; third order condition; second-order parameter; third-order condition
UR - http://eudml.org/doc/273613
ER -

References

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