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On equalities of estimations of parametric functions under a general linear model and its restricted models. (English) Zbl 1197.62020
Summary: Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations of matrices and their generalized inverses. In the past several years, a powerful tool, the matrix rank method was utilized to manipulate various complicated matrix expressions that involve generalized inverses of matrices. We use this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted model.

##### MSC:
 62F10 Point estimation 62J05 Linear regression; mixed models 15A09 Theory of matrix inversion and generalized inverses 62F30 Parametric inference under constraints
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