Empirical tail copulas for functional data

John H. Einmahl and Johan Segers
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Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2021003, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: 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.

Keywords: extreme value statistics; functional data; tail empirical process; tail dependence; tail copula estimation; uniform asymptotic normality (search for similar items in EconPapers)
Date: 2021-01-01
Note: In: Annals of Statistics, , p. to appear (2021)
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2021003

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