# Parametric dependence between random vectors via copula-based divergence measures

## TL;DR

This paper introduces a copula-based framework for quantifying dependence among multiple random vectors, providing new estimators, theoretical properties, and practical applications in finance.

## Contribution

It develops a novel dependence measure using copula-based Phi-divergences, including estimation procedures and asymptotic analysis for both parametric and semi-parametric models.

## Key findings

- Explicit dependence coefficients for Gaussian copulas.
- Asymptotic properties of estimators established.
- Application demonstrated on financial data.

## Abstract

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.