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 for the equality of ordinary least squares and generalized least squares estimators in the linear regression model with firstorder spatial error processes are given.

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we derive different estimators of a parameter associated with the distribution of the...

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...

In this paper we have suggested some improved estimator of parameters of Morgenstern type bivariate logistic distribution (MTBLD) using ranked set sampling. We have shown the superiority of the proposed estimators over Chacko and Thomas (2009) estimators.