Abstract: Three measures of multivariate relationship are revisited. These measures are used to construct nonparametric tests of the null hypothesis of independence of two sets of variables when the parent population distributions are unknown. Their asymptotic distributions are derived under the null hypothesis and under a sequence of alternatives from the asymptotic distribution of covariance and correlation matrices. The tests are illustrated by some examples and a simulation study is performed to compare the tests based on the covariance matrix with those based on the correlation matrix. We also compare these tests to other competitors based on Kendall's matrix and Spearman's matrix.
Keywords: U-statistics, asymptotic distribution, correlation matrix, measures of multivariate association, tests of independence