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Multivariate nonparametric tests in a randomized complete block design |
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| Authors: | J Möttönen J Hüsler |
| Institution: | a Department of Mathematical Sciences Statistics, University of Oulu, P.O. Box 3000, FIN-90014 University of Oulu, Finland b Universität Bern, Institut für Mathematische Statistik und Versicherungslehre, Sidlerstrasse 5, CH-3012 Bern, Switzerland c Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland |
| Abstract: | In this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the multivariate normal and t distribution cases. The tests are rotation invariant only, but affine invariant versions can be easily constructed. The theory is illustrated by an example. |
| Keywords: | 62G10 62G20 62H15 |
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