Parametric dependence between random vectors via copula-based divergence measures
Abstract
This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of -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 , 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.
Cite
@article{arxiv.2302.13611,
title = {Parametric dependence between random vectors via copula-based divergence measures},
author = {Steven De Keyser and Irène Gijbels},
journal= {arXiv preprint arXiv:2302.13611},
year = {2023}
}