Revisiting the BLUE in a Linear Model via Proper Eigenvectors

Jan Hauke (), Augustyn Markiewicz () and Simo Puntanen ()
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Jan Hauke: Adam Mickiewicz University, Institute of Socio-Economic Geography and Spatial Planning
Augustyn Markiewicz: Poznań University of Life Sciences, Department of Mathematical and Statistical Methods
Simo Puntanen: University of Tampere, School of Information Sciences

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 73-83 from Springer

Abstract: Abstract We consider two linear models, and , having different covariance matrices. Our main interest lies in question whether a particular given blue under continues to be a blue under . 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).

Keywords: Best linear unbiased estimator; Gauss–Markov model; Linear model; Löwner ordering; Orthogonal projector; Proper eigenvalues; 15A42; 62J05; 62H12; 62H20 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-81-322-1053-5_7

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