This paper introduces vector copulas  and establishes a vector version of Sklar's theorem. The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non-overlapping multivariate marginals. We construct Elliptical , Archimedean, and Kendall families of vector copulas  and present algorithms to generate data from them. We introduce a concordance ordering for two random vectors with given within-dependence structures and generalize Spearman's rho to random vectors. Finally, we construct empirical vector copulas and show their consistency under mild conditions .
This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of Sklar's theorem. The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non overlapping multivariate marginals. We construct Elliptical and Kendall families of vector copulas , derive their densities, and present algorithms to generate data from them. The use of vector copulas is illustrated with a stylized analysis of international financial contagion .
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associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation,
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non-overlapping
non overlapping
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, Archimedean,
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, derive their densities,
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We introduce a concordance ordering for two random vectors with given within-dependence structures and generalize Spearman's rho to random vectors. Finally, we construct empirical vector copulas and show their consistency under mild conditions
The use of vector copulas is illustrated with a stylized analysis of international financial contagion