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...

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...

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>

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.

We consider in this paper a partitioned linear model<formula format="inline"><simplemath>&lcub;y,  X₁β₁&plus;X₂β_{2</su b>,  σ-super-2σ&rcub;</simplemath></formula>and two corresponding small models<formula format="inline"><simplemath>&lcub;y,  X₁β₁,  σ-super-2σ&rcub;</simplemath></formula>and<formula format="inline"><simplemath>&lcub;y,  X₂β₂,  σ-super-2σ&rcub;</simplemath></formula>. We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full...<//su>}