Abstract
Coefficients like Kendall's tau or Spearman's rho, used to measure (strength of) an association between two random variables, were thoroughly studied and described in the middle of 20th century. Requirements on bivariate association measures are well-known.
However, generalization of such measures into higher dimensions is not very straightforward and brings discussion on the desirable properties. In addition, bivariate measures can be often generalized in multiple manners.
We discuss methods of generalization, their theoretical properties, strengths and weaknesses. In particular, behavior of association measures when dimension grows to infinity is of interest.
Moreover, examples illustrate the performance and use of such measures.