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.

翻译：本文推广了2-Wasserstein依赖性系数，用于度量有限个随机向量之间的依赖性。该推广包含了理论性质，特别是聚焦于最大依赖性的解释，以及在高斯copula假设下所提出的半参数估计量的渐近正态性结果。此外，我们讨论了多个随机向量之间依赖性度量的通用公理、其他合理的归一化方法及多种实例。随后，我们研究了基于惩罚经验协方差矩阵的插件估计量，以应对高维问题，并通过引入（块）稀疏性来考虑可能的边际独立性。通过模拟研究，我们考察了后一种思想，并与其他依赖性系数进行了比较。最后，我们在两个实际数据应用中展示了所开发方法的实用性。