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

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 nonstandard.

Citation

Download Citation

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

Information

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

Digital Object Identifier: 10.1214/21-AOS2050

Subjects:
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

JOURNAL ARTICLE
25 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 5 • October 2021
Back to Top