We study relations between the weighted least-squares estimators (WLSEs) of given parametric functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbf{K}_1\varvec{\beta }_1 + \mathbf{K}_2\varvec{\beta }_2$$</EquationSource> </InlineEquation> under a general partitioned linear model <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\fancyscript{M}}=\{ \mathbf{y}, \, \mathbf{X}_1\varvec{\beta }_1 +...</equationsource></inlineequation></equationsource></inlineequation>

Necessary and sufficient conditions are derived for the BLUE in a general multiple-partitioned linear model to be the sum of the BLUEs under the k small models , ..., . Some consequences and further research topics are also given.

Projectors associated with a particular estimator in a general linear model play an important role in characterizing statistical properties of the estimator. A variety of new properties were derived on projectors associated with the weighted least-squares estimator (WLSE). These properties...

Seemingly unrelated regression models are extensions of linear regression models which allow correlated errors between equations. Estimations and inferences of singular seemingly unrelated regression models involve some complicated operations of the given matrices in the models and their...

Equality and proportionality of the ordinary least-squares estimator (OLSE), the weighted least-squares estimator (WLSE), and the best linear unbiased estimator (BLUE) for X[beta] in the general linear (Gauss-Markov) model are investigated through the matrix rank method.