Efficiency Robust Two-Sample Rank Tests
Abstract In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has a uniformly better local power performance (risk point) for a specified class A of distribution function alternatives F. Such rank tests may be constructed using formal Bayes procedures resulting in convex mixtures of the locally most powerful rank tests TF for FeΛ. Asymptotic relative efficiency (ARE) calculations uncover the symmetry relation ARE (TF, TF *; F) = ARE (TF *,TF; F*). Examples involving Logistic, Normal and Double Exponential are considered.