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Robust Estimators in Generalized Pareto Models

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  • Peter Ruckdeschel

    (Fraunhofer ITWM, Department of Financial Mathematics, Dept. of Mathematics, Univerisity of Kaiserslautern)

  • Nataliya Horbenko

    (Fraunhofer ITWM, Department of Financial Mathematics, Dept. of Mathematics, Univerisity of Kaiserslautern)

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    Abstract

    This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.

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    File URL: http://arxiv.org/pdf/1005.1476
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1005.1476.

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    Date of creation: May 2010
    Date of revision: Sep 2011
    Handle: RePEc:arx:papers:1005.1476

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    Web page: http://arxiv.org/

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