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Quadratic estimators of covariance components in a multivariate mixed linear model. (English) Zbl 1405.62099

Summary: It is known that Method III of C. R. Henderson [“Estimation of variance and covariance components”, Biometrics 9, No. 2, 226–252 (1953; doi:10.2307/3001853)] 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 W. Kruskal [Ann. Math. Stat. 39, 70–75 (1968; Zbl 0162.21902)] and M. L. Eaton [Ann. Math. Stat. 41, 528–538 (1970; Zbl 0195.20101)]. 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.

MSC:

62J10 Analysis of variance and covariance (ANOVA)
62J05 Linear regression; mixed models
62F10 Point estimation
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References:

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