October 2021 Empirical tail copulas for functional data
John H. J. Einmahl, Johan Segers
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Ann. Statist. 49(5): 2672-2696 (October 2021). DOI: 10.1214/21-AOS2050


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 nonstandard.


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John H. J. Einmahl. Johan Segers. "Empirical tail copulas for functional data." Ann. Statist. 49 (5) 2672 - 2696, October 2021. https://doi.org/10.1214/21-AOS2050


Received: 1 January 2020; Revised: 1 October 2020; Published: October 2021
First available in Project Euclid: 12 November 2021

MathSciNet: MR4338379
zbMATH: 1486.62140
Digital Object Identifier: 10.1214/21-AOS2050

Primary: 62G05 , 62G20 , 62G30 , 62G32 , 62M99
Secondary: 60F17 , 60G70

Keywords: Extreme value statistics , functional data , tail copula estimation , tail dependence , tail empirical process , uniform asymptotic normality

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 5 • October 2021
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