On Asymptotic Relative Efficiencies of a Class of Rank Tests
Joseph L. Gastwirth · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1970
Summary A partial ordering is introduced in a class of rank tests according to the weight or emphasis they place on the middle ranks versus the extreme ones. This notion of order is shown to be related to van Zwet's partial ordering of symmetric densities according to the probability in their tails. Bounds on Pitman's asymptotic relative efficiency (a.r.e.) of several tests to the Wilcoxon test are established. Finally, a sharp lower bound for the asymptotic power of the Ψ-test is obtained.