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Change point analysis of extreme values

Authors

  • G. Dierckx,

    Corresponding author
    1. Department of Mathematics, Hogeschool Universiteit Brussel, Stormstraat, B-1000 Brussel, Belgium
    2. Departement of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium
    • Department of Mathematics, Hogeschool Universiteit Brussel, Stormstraat, B-1000 Brussel, Belgium and Departement of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium.
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  • J. L. Teugels

    1. Departement of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium
    2. EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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  • This article is published in Environmetrics as a special issue on TIES 2008: Quantitative Methods for Environmental Sustainability, edited by Sylvia R. Esterby, University of British Columbia Okanagan, Canada.

Abstract

In a sample from the distribution of a random variable, it is possible that the tail behavior of the distribution changes at some point in the sample. This tail behavior can be described by absolute or relative excesses of the data over a high threshold, given that the random variable exceeds the threshold. The limit distribution of the absolute excesses is given by a generalized Pareto distribution with an extremal parameter γ and a scale parameter σ. When the extreme value index γ is positive, then the relative excesses can be described in the limit by a Pareto distribution with this index as parameter.

In this paper we concentrate on testing whether changes occur in the value of the extreme value index γ and/or the scale parameter. To this end, appropriate test statistics are introduced based on the likelihood approach for independent data. Asymptotic properties of these test statistics are studied leading to adequate critical values. After giving a practical test procedure, we apply our results to a series of simulations and real life examples. Copyright © 2010 John Wiley & Sons, Ltd.

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