  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.
