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Moment-based estimation of extendible Marshall-Olkin copulas

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Abstract

Associated with any parametric family of Lévy subordinators there is a parametric family of extendible Marshall-Olkin copulas, which shares the dependence structure with the vector of first passage times of the Lévy subordinator across i.i.d. exponential threshold levels. The present article derives a strongly consistent and asymptotically normal estimator for the parameters in such models. The estimation strategy is to minimize the Euclidean distance between certain empirical and theoretical functionals of the distribution. As a byproduct, the covariance structure of the order statistics of a d-dimensional extendible Marshall-Olkin distribution is computed.

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Authors and Affiliations

  1. Institut für Zahlentheorie und Wahrscheinlichkeitstheorie, Universität Ulm, 89069, Ulm, Germany

    Christian Hering

  2. Assenagon Credit Management GmbH i.G., Franziska-Bilek-Weg 9, 80339, München, Germany

    Jan-Frederik Mai

Authors
  1. Christian Hering
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  2. Jan-Frederik Mai
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Correspondence to Christian Hering.

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Hering, C., Mai, JF. Moment-based estimation of extendible Marshall-Olkin copulas. Metrika 75, 601–620 (2012). https://doi.org/10.1007/s00184-011-0344-x

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  • DOI: https://doi.org/10.1007/s00184-011-0344-x

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