  Following our previous work on copula-based nonsymmetric bivariate dependence
measures, we propose a new set of conditions on nonsymmetric multivariate
dependence measures which characterize both independence and complete
dependence of one random variable on a group of random variables. The measures
are nonparametric in that they are copula-based and are invariant under
continuous bijective transformations on the group of random variables. We also
construct explicitly new measures that satisfy the conditions. Besides, we
extend the star product on bivariate copulas to multivariate copulas and prove
the DPI condition and self-equitability for the new measures. A further
extension to measures of dependence of one group of random variables on another
group of random variables is also discussed.
