, Volume 21, Issue 2, pp 205–233 | Cite as

A continuous updating weighted least squares estimator of tail dependence in high dimensions

  • John H. J. Einmahl
  • Anna KirilioukEmail author
  • Johan Segers


Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis of a goodness-of-fit statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.


Brown–Resnick process Extremal coefficient Max-linear model Multivariate extremes Stable tail dependence function 

AMS 2000 Subject Classifications

Primary–62G32 62G05 62G10 62G20 Secondary–60F05 60G70 


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The research by A. Kiriliouk was funded by a FRIA grant of the “Fonds de la Recherche Scientifique – FNRS” (Belgium). J. Segers gratefully acknowledges funding by contract “Projet d’Actions de Recherche Concertées” No. 12/17-045 of the “Communauté française de Belgique” and by IAP research network Grant P7/06 of the Belgian government (Belgian Science Policy).


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Econometrics & OR and CentERTilburg UniversityLE TilburgThe Netherlands
  2. 2.Institut de Statistique, Biostatistique et Sciences ActuariellesUniversité catholique de LouvainLouvain-la-NeuveBelgium

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