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An M-Estimator for Tail Dependence in Arbitrary Dimensions

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Author Info

  • Einmahl, J.H.J.
  • Krajina, A.
  • Segers, J.

    (Tilburg University, Center for Economic Research)

Abstract

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-013.

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Date of creation: 2011
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Handle: RePEc:dgr:kubcen:2011013

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Web page: http://center.uvt.nl

Related research

Keywords: asymptotic statistics; factor model; M-estimation; multivariate extremes; tail dependence;

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References

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  1. de Haan, Laurens & Neves, Cláudia & Peng, Liang, 2008. "Parametric tail copula estimation and model testing," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1260-1275, July.
  2. Y. Malevergne & D. Sornette, 2002. "Tail Dependence of Factor Models," Papers cond-mat/0202356, arXiv.org.
  3. Fama, Eugene F & French, Kenneth R, 1996. " Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March.
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Cited by:
  1. Marta Ferreira & Helena Ferreira, 2013. "Extremes of multivariate ARMAX processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(4), pages 606-627, November.
  2. Carsten Bormann & Melanie Schienle & Julia Schaumburg, 2014. "A Test for the Portion of Bivariate Dependence in Multivariate Tail Risk," Tinbergen Institute Discussion Papers 14-024/III, Tinbergen Institute.
  3. Fougères, Anne-Laure & Mercadier, Cécile & Nolan, John P., 2013. "Dense classes of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 109-129.
  4. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2012. "International diversification: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 871-885.

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