Conditional empirical copula processes and generalized dependence measures

TL;DR

This paper investigates the weak convergence of conditional empirical copula processes with nonzero conditioning probability, validates bootstrap methods, and introduces generalized dependence measures with asymptotic normality results.

Contribution

It provides theoretical foundations for the weak convergence of conditional empirical copula processes and introduces new generalized dependence measures with proven asymptotic properties.

Findings

Bootstrap schemes are validated for conditional empirical copula processes.

Asymptotic normality of estimators for generalized dependence measures is established.

Theoretical results support the use of these measures in multivariate dependence analysis.

Abstract

We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general - possibly conditional - multivariate dependence measures and their estimators. By applying our theoretical results, we prove the asymptotic normality of some estimators of such dependence measures.