High-dimensional copula-based Wasserstein dependence

The aim is to generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence and an asymptotic normality result for a proposed semi-parametric estimator under a Gaussian copula assumption. In addition, it is of interest to look at general axioms for dependence measures between multiple random vectors, at plausible normalizations, and at various examples. Afterwards, it is important to study plug-in estimators based on penalized empirical covariance matrices in order to deal with high dimensionality issues and taking possible marginal independencies into account by inducing (block) sparsity. The latter ideas are investigated via a simulation study, considering other dependence coefficients as well. The use of the developed methods is illustrated in two real data applications.