Robust estimation of the generalized Pareto distribution
Robust estimation of the generalized Pareto distribution
One approach used for analysing extremes is to fit the excesses over a high threshold by a generalized Pareto distribution. For the estimation of the shape and scale parameters in the generalized Pareto distribution, under some restrictions on the value of the scale parameter, maximum likelihood, method of moments and probability-weighted moments' estimators are available. However, these are not robust estimators. In this paper we implement a robust estimation procedure known as the method of medians (He and Fung (1999)) to estimate the parameters in the generalized Pareto distribution. The asymptotic distribution of our estimator is normal for any value of the shape parameter except -1.
generalized Pareto distribution, high threshold, maximum likelihood estimation, method of medians, method of moments, probability-weighted moments’ estimation, robust estimation
53-65
Peng, L.
4c503346-f97c-4980-a799-d531907e1734
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
2001
Peng, L.
4c503346-f97c-4980-a799-d531907e1734
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
Peng, L. and Welsh, A.H.
(2001)
Robust estimation of the generalized Pareto distribution.
Extremes, 4 (1), .
Abstract
One approach used for analysing extremes is to fit the excesses over a high threshold by a generalized Pareto distribution. For the estimation of the shape and scale parameters in the generalized Pareto distribution, under some restrictions on the value of the scale parameter, maximum likelihood, method of moments and probability-weighted moments' estimators are available. However, these are not robust estimators. In this paper we implement a robust estimation procedure known as the method of medians (He and Fung (1999)) to estimate the parameters in the generalized Pareto distribution. The asymptotic distribution of our estimator is normal for any value of the shape parameter except -1.
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Published date: 2001
Keywords:
generalized Pareto distribution, high threshold, maximum likelihood estimation, method of medians, method of moments, probability-weighted moments’ estimation, robust estimation
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Statistics
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Local EPrints ID: 29936
URI: http://eprints.soton.ac.uk/id/eprint/29936
ISSN: 1386-1999
PURE UUID: 5ecf5f51-57f6-4889-811d-2f30b1e47e08
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Date deposited: 11 May 2006
Last modified: 11 Dec 2021 15:16
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Contributors
Author:
L. Peng
Author:
A.H. Welsh
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