An M-estimator for tail dependence in arbitrary dimensions

Einmahl, John H. J.;Krajina, Andrea;Segers, Johan
(2012) Annals of Statistics — Vol. 40, n° 3, p. 1764-1793 (2012)

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Authors
  • Einmahl, John H. J.Tilburg University, The Netherlands
    Author
  • Krajina, AndreaUniversity of Göttingen, Germany
    Author
  • Segers, JohanUCLouvain
    Author
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 minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization 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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Einmahl, J. H. J., Krajina, A., & Segers, J. (2012). An M-estimator for tail dependence in arbitrary dimensions. Annals of Statistics, 40(3), 1764-1793. https://doi.org/10.1214/12-AOS1023 (Original work published 2012)