Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U -statistics. In addition such a symbolic method can be naturally extended to multivariate case, i.e. to generalized k-statistics.

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 Spearmantype test statistics is made. Conditions for Pitman optimality of the test are established. Examples that illustrate the quality o...

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