Affine equivariant multivariate rank methods. (English) Zbl 1011.62053

Summary: The classical multivariate statistical methods (MANOVA, principal components analysis, multivariate multiple regression, canonical correlations, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations.
In this paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. The affine equivariant multivariate rank concept is based on the multivariate H. Oja [Stat. Probab. Lett. 1, 327-332 (1983; Zbl 0517.62051)] median.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
62J10 Analysis of variance and covariance (ANOVA)
62H20 Measures of association (correlation, canonical correlation, etc.)
62J05 Linear regression; mixed models


Zbl 0517.62051
Full Text: DOI


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