The necessary and sufficient conditions for the weighted least-squares estimators (WLSEs) of parametric functions K1β1+K2β2+⋯+Kmβm under a multiple partitioned linear model ℳ={y,X1β1+⋯+Xmβm,σ2Σ} to be the sum of the WLSEs of Kiβi under the m small models...

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>