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Robust Estimation of the Generalized Pareto Distribution

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Abstract

One approach used for analyzing 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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Authors and Affiliations

  1. Centre for Mathematics and its Applications, Australian National University, Australia

    Liang Peng & A.H. Welsh

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Liang Peng

  3. Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UK

    A.H. Welsh

Authors
  1. Liang Peng
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  2. A.H. Welsh
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Peng, L., Welsh, A. Robust Estimation of the Generalized Pareto Distribution. Extremes 4, 53–65 (2001). https://doi.org/10.1023/A:1012233423407

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  • DOI: https://doi.org/10.1023/A:1012233423407

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