Open Access
2022 Conditional empirical copula processes and generalized measures of association
Alexis Derumigny, Jean-David Fermanian
Author Affiliations +
Electron. J. Statist. 16(2): 5692-5719 (2022). DOI: 10.1214/22-EJS2075


We study the weak convergence of conditional empirical copula processes indexed by general families of conditioning events that have non zero probabilities. Moreover, we also study the case where the conditioning events are chosen in a data-driven way. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general multivariate measures of association, possibly given some fixed or random conditioning events. By applying our theoretical results, we prove the asymptotic normality of the estimators of such measures. We illustrate our results with financial data.

Funding Statement

Jean-David Fermanian’s work has been supported by the labex Ecodec (reference project ANR-11-LABEX-0047).


The authors warmly thank the Associate Editor and two reviewers whose numerous remarks and suggestions allowed us to strongly improve the paper.


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Alexis Derumigny. Jean-David Fermanian. "Conditional empirical copula processes and generalized measures of association." Electron. J. Statist. 16 (2) 5692 - 5719, 2022.


Received: 1 February 2022; Published: 2022
First available in Project Euclid: 25 October 2022

MathSciNet: MR4499842
zbMATH: 07633925
Digital Object Identifier: 10.1214/22-EJS2075

Primary: 62G05 , 62G30
Secondary: 62G09 , 62H20

Keywords: bootstrap , conditional copula , empirical copula process , weak convergence

Vol.16 • No. 2 • 2022
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