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>

We derive an expression for the variance matrix of the vector of (uncentered) sample second-order moments under multivariate linear relations and an independence assumption. An application of the result is presented.

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test...