Empirical tail copulas for functional data

J.H.J. Einmahl, J. Segers

Research output: Contribution to journalArticleScientificpeer-review


For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to continuous functional data by establishing the asymptotic normality of the estimators of the tail copula, uniformly over all finite subsets of at most D points (D fixed). An application for testing tail copula stationarity is presented. The main tool for deriving the result is the uniform asymptotic normality of all the D-variate tail empirical processes. The proof of the main result is non-standard.
Original languageEnglish
Pages (from-to)2672-2696
JournalThe Annals of Statistics
Issue number5
Publication statusPublished - Oct 2021


  • extreme value statistics
  • functional data
  • tail empirical process
  • tail dependence
  • tail copula estimation
  • uniform asymptotic normality


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