We consider equalities between the ordinary least squares estimator (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathrm {OLSE} $$</EquationSource> </InlineEquation>), the best linear unbiased estimator (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathrm {BLUE} $$</EquationSource> </InlineEquation>) and the best linear unbiased predictor (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\mathrm {BLUP} $$</EquationSource> </InlineEquation>) in the general linear model <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\{ \mathbf y , \mathbf X \varvec{\beta }, \mathbf...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

We briefly discuss the so called pseudo-GLS estimator in a standard linear regression model with nonsperical disturbances, and conclude that the potentiality for applications is higher than originally assumed by Fiebig Bartels and Kramer (1996).