This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of $Phi$, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.

翻译：本文通过$Phi$-散度族，提出了对可能具有不同大小的多组随机变量进行基于copula的依赖性量化方法。为此，本文首先建立了一个公理化框架，随后聚焦于假设copula密度存在的绝对连续情形。我们考虑了参数和半参数框架，讨论了估计流程，并报告了所提估计量的渐近性质。具体而言，我们首先聚焦于高斯copula方法，该方法针对特定$Phi$选择能导出显式且具有吸引力的依赖性系数，更易于估计。其次，我们考虑了广义参数copula族，特别关注嵌套阿基米德copula，它是随机向量依赖性建模的自然选择。通过实例说明了结果，并提供了模拟实验及金融数据的真实应用案例。