Miltivariate measures of dependence based on copulas

The paper is devoted to the multivariate measures of dependence. In contrast to the classical approach, where the pairs of variables are studied, we investigate the dependence of more than two variables. We mainly consider the measures based on copulas. These are the multivariable generalizations of the known coefficients of such correlation as Spearman’s rho, Kendall’s tau, Blomquist’s beta and Gini’s gamma. We present the definitions, the constructions and the basic properties of such multivariate measures of dependence. The case of large number of dimension, greater than two, presents more complications. We have several different versions of such generalization in this case and the lower bound of the values of such measures of dependence are close to zero. We also study the multivariate tail dependences. The last part of the paper is devoted to the estimation of multivariable versions of Spearman’s rho coefficient.