Krämer (Sankhy<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\bar{\mathrm{a }}$$</EquationSource> </InlineEquation> 42:130–131, <CitationRef CitationID="CR13">1980</CitationRef>) posed the following problem: “Which are the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbf{y}$$</EquationSource> </InlineEquation>, given <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\mathbf{X}$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mathbf{V}$$</EquationSource> </InlineEquation>, such that OLS and Gauss–Markov are equal?”. In other words, the problem aimed at identifying those vectors <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\mathbf{y}$$</EquationSource> </InlineEquation>...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></citationref></equationsource></inlineequation>

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>

Necessary and sufficient conditions are given for a restricted growth curve model to be consistent. The general expressions of the weighted least-squares estimators (WLSEs), the ordinary least-squares estimators (OLSEs) and the best linear unbiased estimator (BLUE) under this model are also...

It is well-known, in the literature, that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. In the present paper, we consider the functional equation <Equation ID="Equa"> <EquationSource Format="TEX">$$F(x)=F(xy) + F(xQ(y)), \quad...</equationsource></equation>