Abstract: Recently
Borroni and Zenga [3] proposed a new nonparametric test for independence; the
corresponding test-statistic is
based on Gini’s mean difference computed on the total ranks obtained on the
basis of two rankings of a sample of nunits.
The considered test is a competitor of classical tools such as Spearman’s rho,
Kendall’s tau and Gini’s cograduation index. While some research work has
been done to evaluate the performance of in
small samples, this paper reports some further asymptotical results. The Pitman
asymptotic relative efficiency (ARE) of with
respect to its competitors is computed for the Fairlie-Gumbel-Morgenstern
distribution. In addition, some simulation results are reported for other
families of distribution where the computation of the ARE poses some technical
difficulties.
