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Statistical Methods and Applications

, Volume 16, Issue 3, pp 347–356 | Cite as

Quadratic estimators of covariance components in a multivariate mixed linear model

  • Gabriela BeganuEmail author
Original Article

Abstract

It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist 39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model.

Keywords

Linear operator Orthogonal projection Quadratic form Generalized least squares estimator Estimable parametric function 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsAcademy of Economic StudiesBucharestRomania

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