The Asymptotic Efficacies and Relative Efficiencies of Various Linear Rank Tests for Independence

In this paper we consider eight general models of independence, the Hájek–Šidák model, the Janssen–Mason model, Konijn’s model, Steffensen’s model, the Farlie model, the bivariate Gamma distribution, the Mardia model and the Frechet model. The asymptotic efficacies and relative efficiencies of various linear rank tests are computed. It turns out that the asymptotic power depends heavily on the underlying model. However, for the vast majority of considered models, the Spearman test is, asymptotically, a good choice.