The BLUE's covariance matrix revisited: A review

DOI10.1016/j.jspi.2008.03.029zbMath1141.62325OpenAlexW2033210693MaRDI QIDQ928907

George P. H. Styan, Jarkko Isotalo, Simo Puntanen

Publication date: 11 June 2008

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2008.03.029

zbMATH Keywords

linear modelarithmetic meangeneralized inverseresidualsorthogonal projectorbest linear unbiased estimator (BLUE)canonical correlationsWatson efficiencyminimum variance linear unbiased estimatorordinary least squares estimator (OLSE)proper eigenvalues

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Measures of association (correlation, canonical correlation, etc.) (62H20)

Related Items (4)

Some equalities and inequalities for covariance matrices of estimators under linear model ⋮ Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model ⋮ Matrix rank and inertia formulas in the analysis of general linear models ⋮ Estimability of variance components when all model matrices commute

Cites Work

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• Spectrum and trace invariance criterion and its statistical applications
• Some properties of BLUE in a linear model and canonical correlations associated with linear transformations
• On a separation theorem for generalized eigenvalues and a problem in the analysis of sample surveys
• Some results on proper eigenvalues and eigenvectors with applications to scaling
• Shorted operators and generalized inverses of matrices
• Generalized eigenvalue problems with positive semi-definite matrices
• Canonical correlations associated with symmetric reflexive generalized inverses of the dispersion matrix
• A note on multiple and canonical correlation for a singular covariance matrix
• A conversation with T. W. Anderson
• SERIAL CORRELATION IN REGRESSION ANALYSIS. I
• A further note on a theorem on the difference of the generalized inverses of two nonnegative definite matrices
• Inefficiency and correlation
• The Shorted Operator Statistically Interpreted
• Shorted Operators. II
• When is the Arithmetic Mean Blue?
• On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models
• Shorted Operators
• Inequalities: theory of majorization and its applications

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