Covariance structure analysis of nonnormal data is important because in practice all data are nonnormal. When applying covariance structure analysis to nonnormal data, it is generally assumed that the asymptotic covariance matrix Γ for the nonredundant terms in the sample covariance matrix S is...

It is shown that for any full column rank matrix X <Subscript>0</Subscript> with more rows than columns there is a neighborhood <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal{N}$</EquationSource> </InlineEquation> of X <Subscript>0</Subscript> and a continuous function f on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal{N}$</EquationSource> </InlineEquation> such that f(X) is an orthogonal complement of X for all X in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal{N}$</EquationSource> </InlineEquation>. This is used to derive a distribution free...</equationsource></inlineequation></equationsource></inlineequation></subscript></equationsource></inlineequation></subscript>