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Revisiting the BLUE in a linear model via proper eigenvectors. (English) Zbl 06177514
Bapat, Ravindra B. (ed.) et al., Combinatorial matrix theory and generalized inverses of matrices. New Delhi: Springer (ISBN 978-81-322-1052-8/hbk; 978-81-322-1053-5/ebook). 73-83 (2013).
Summary: We consider two linear models, $$\mathcal M_1 = \mathbf{\{y, X \beta, V_1\}}$$ and $$\mathcal M_2 = \mathbf{\{y, X \beta, V_2\}}$$, having different covariance matrices. Our main interest lies in question whether a particular given blue under $$\mathcal M_1$$ continues to be a blue under $$\mathcal M_2$$. We give a thorough proof of a result originally due to Mitra and Moore (Sankhyā, Ser. A 35:139–152, 1973). While doing this, we will review some useful properties of the proper eigenvalues in the spirit of Rao and Mitra (Generalized Inverse of Matrices and Its Applications, 1971).
For the entire collection see [Zbl 1261.15001].

##### MSC:
 62 Statistics 15A42 Inequalities involving eigenvalues and eigenvectors 62J05 Linear regression; mixed models 62H12 Estimation in multivariate analysis 62H20 Measures of association (correlation, canonical correlation, etc.)
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