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February 2017 Weak convergence of the empirical copula process with respect to weighted metrics
Betina Berghaus, Axel Bücher, Stanislav Volgushev
Bernoulli 23(1): 743-772 (February 2017). DOI: 10.3150/15-BEJ751


The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop asymptotic theory for estimators of dependence measures or copula densities, they allow to derive tests for stochastic independence or specific copula structures, or they may serve as a fundamental tool for the analysis of multivariate rank statistics. In the present paper, we establish weak convergence of the empirical copula process (for observations that are allowed to be serially dependent) with respect to weighted supremum distances. The usefulness of our results is illustrated by applications to general bivariate rank statistics and to estimation procedures for the Pickands dependence function arising in multivariate extreme-value theory.


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Betina Berghaus. Axel Bücher. Stanislav Volgushev. "Weak convergence of the empirical copula process with respect to weighted metrics." Bernoulli 23 (1) 743 - 772, February 2017.


Received: 1 November 2014; Revised: 1 June 2015; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 1367.60026
MathSciNet: MR3556791
Digital Object Identifier: 10.3150/15-BEJ751

Keywords: bivariate rank statistics , empirical copula process , Pickands dependence function , strongly mixing , weighted weak convergence

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 1 • February 2017
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