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Identifying groups of variables with the potential of being large simultaneously

  • Maël ChiapinoEmail author
  • Anne Sabourin
  • Johan Segers


Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric, rank-based estimators of these coefficients justifies a stopping criterion in an algorithm that searches the collection of all possible groups of variables in a systematic way, from smaller groups to larger ones. The issue that the tolerance level in the stopping criterion should depend on the size of the groups is circumvented by the use of a conditional tail dependence coefficient. Alternatively, such stopping criteria can be based on limit distributions of rank-based estimators of the coefficient of tail dependence, quantifying the speed of decay of joint survival functions. A performance score calculated by ten-fold cross-validation allows the user to select one among the various algorithms and set its tuning parameters in a data-driven way.


Multivariate extremes Asymptotic dependence Statistical tests High dimensional data 

AMS 2000 Subject Classifications

MSC 62G32 MSC 62H15 MSC 62H05 MSC 62H20 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LTCI, Télécom ParisTechUniversité Paris-SaclayParisFrance
  2. 2.Institut de Statistique, Biostatistique et Sciences ActuariellesUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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