Assume that an original general linear model is misspecified by adding some new regressors. We investigate in such a case relationships between the best linear unbiased estimators under the two models. In particular, we give necessary and sufficient conditions for the best linear unbiased...

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>