On asymptotic efficiency of multivariate version of Spearman's rho

A multivariate version of Spearman’s rho for testing independence is considered. Its asymptotic efficiency is calculated under a general distribution model specified by the dependence function. The efficiency comparison study that involves other multivariate Spearman-type test statistics is made. Conditions for Pitman optimality of the test are established. Examples that illustrate the quality of the multivariate Spearman’s test are included.