, Volume 17, Issue 3, pp 387–410 | Cite as

CRPS M-estimation for max-stable models

  • Robert YuenEmail author
  • Stilian Stoev


Max-stable processes provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods which has motivated use of composite likelihood methods Padoan et al. (J. Amer. Stat. Assoc. 105(489):263–277, 2010). In contrast, the finite dimensional cumulative distribution functions (CDFs) appear natural to work with, and are readily available or can be approximated well. Motivated by this fact, in this work we develop an M-estimation framework for max-stable models based on the continuous ranked probability score (CRPS) of multivariate CDFs. We start by establishing conditions for the consistency and asymptotic normality of the CRPS-based estimators in a general context. We then implement them in the max-stable setting and provide readily computable expressions for their asymptotic covariance matrices. The resulting point and asymptotic confidence interval estimates are illustrated over popular simulated models. They enjoy accurate coverages and offer an alternative to composite likelihood based methods.


Max-stable Multivariate extremes M-estimation CRPS 

AMS 2000 Subject Classifications



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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Statistics University of MichiganUniversity of MichiganAnn ArborUSA

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