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Sign and rank covariance matrices with applications to multivariate analysis (Diss.). (English) Zbl 1137.62339

From the introduction: This dissertation consists of five original publications. The papers consider the statistical properties (consistency, limiting distribution, limiting efficiencies, robustness, computation, estimation of accuracy) of the affine equivariant sign and rank covariance matrix introduced by S. Visuri, V. Koivunen and H. Oja [J. Stat. Plann. Inference 91, No. 2, 557–575 (2000; Zbl 0965.62049)] and their use in multivariate analysis. In particular, new estimates for principal component analysis and for multivariate linear regression are proposed and their statistical properties are derived. The concepts of multivariate sign and rank are based on Oja’s criterion function.

MSC:

62H12 Estimation in multivariate analysis
62H25 Factor analysis and principal components; correspondence analysis
62-02 Research exposition (monographs, survey articles) pertaining to statistics

Citations:

Zbl 0965.62049
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