ON THE EFFICIENCY OF MULTIVARIATE SPATIAL SIGN AND RANK TESTS

conditionally and asymptotically distribution-free rotation but not scale invariant competitors of the well known Hotelling's T 2 tests. In this paper efficiency results are found in the one-sample location case, but they natu- rally hold in the multivariate two-sample, multisample and general linear model case. . The lack of means of fully ordering or ranking observations in the multivariate setting seems at first sight to be an obstacle to generalizing the concepts of sign and rank and signed-rank. However, these concepts can be defined also by using L criterion functions as follows. Consider k- 1 < < variate observations y , . . . , y . Utilizing the Euclidean distance y s 1 N 2 2 . 1r2 y q ??? qy , the three objective functions 1 k < < T y s S y y , . i i i i i

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