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...