A set of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation>-principal points of a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>p</mi> </mrow> </math> </EquationSource> </InlineEquation>-dimensional distribution is an optimal <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation>-point-approximation of the distribution in terms of a squared error loss. It is in general difficult to derive an explicit expression of principal points. Hence, we may have to...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

This paper presents a generalization of Rao's covariance structure. In a general linear regression model, we classify the error covariance structure into several categories and investigate the efficiency of the ordinary least squares estimator (OLSE) relative to the Gauss-Markov estimator (GME)....

In a seemingly unrelated regression model with p([greater-or-equal, slanted]2) equations, this paper considers the problem of testing independence of equations against a one-sided alternative hypothesis. The power functions of invariant tests are evaluated and the locally most mean powerful...