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Affine invariant multivariate sign and rank tests. (English) Zbl 0938.62063
Multivariate extensions of the concepts of sign, rank and signed-rank are considered. The extensions based on the generalized affine equivariant median of H. Oja [Stat. Probab. Lett. 1, 327-332 (1983; Zbl 0517.62051)] with natural analogues of one-sample, two-sample and multisample sign and rank tests, affine equivariant median and Hodges-Lehmann-type estimates are reviewed. The aim is to develop tests and estimates in the general multivariate linear model case. Some comparisons are made to other generalizations. The theory is illustrated by two examples.

MSC:
62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
62H12 Estimation in multivariate analysis
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