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.
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.
Alexis Derumigny. Jean-David Fermanian. "Conditional empirical copula processes and generalized measures of association." Electron. J. Statist. 16 (2) 5692 - 5719, 2022. https://doi.org/10.1214/22-EJS2075