Abstract
For general multivariate linear models, a composite hypothesis does not usually induce invariance of the joint distribution under appropriate groups of transformations, so that genuinely distribution-free tests do not usually exist. For this purpose, some aligned rank order statistics are incorporated in the proposal and study of a class of asymptotically distribution-free tests. Tests for the parallelism of several multiple regression surfaces are also considered. Finally the optimal properties of these tests are discussed.
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Work supported by the Air Force Office of Scientific Research, AFSC, USAF, Contract Nos: AFOSR-74-2736 and AFOSR-76-2927. Reproduction in whole or part is permitted for any purpose of the U.S. Government
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Sen, P.K., Puri, M.L. Asymptotically distribution-free aligned rank order tests for composite hypotheses for general multivariate linear models. Z. Wahrscheinlichkeitstheorie verw Gebiete 39, 175–186 (1977). https://doi.org/10.1007/BF00535470
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DOI: https://doi.org/10.1007/BF00535470