ON AFFINE INVARIANT SIGN AND RANK TESTS IN ONE AND TWO SAMPLE MULTIVARIATE PROBLEMS

Some extensions of sign and rank tests for multivariate problems are proposed and studied. Unlike coordinatewise sign and rank tests considered by some earlier authors, our approach is affine invariant, an it is based on a transformation retransformation strategy introduced by Chakraborty and Chaudhuri (1996, 1998). Affine invariance is expected to lead to superior statistical performance of our procedures especially in the presence of high correlations among the coordinate variables in multivariate data sets. This fact is amply demonstrated using analytic studies as well as Monte Carlo simulations. We also propose a multivariate version of Hodges-Lehmann estimate, which is affine equivariant and have interesting statistical properties. Some real data sets have been analyzed to demonstrate the performance of the proposed methodology.