  We 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, we
discuss general axioms for dependence measures between multiple random vectors,
other plausible normalizations, and various examples. Afterwards, we look into
plug-in estimators based on penalized empirical covariance matrices in order to
deal with high dimensionality issues and take possible marginal independencies
into account by inducing (block) sparsity. The latter ideas are investigated
via a simulation study, considering other dependence coefficients as well. We
illustrate the use of the developed methods in two real data applications.
