Assessing multivariate nonnormality using univariate distributions

Abstract

SUMMARY This paper proposes diagnostics that can indicate regions where multivariate distributions are poorly behaved in the sense that they are far from normal. The measure of nonnormality developed by Slate (1994) for univariate distributions is extended to multivariate parametric models by application to univariate marginal and conditional distributions. The approach is illustrated for univariate conditional distributions using dynamic graphics in Xlisp-Stat (Tierney, 1990). Examples show that the exploratory look at 'slices' through the multidimensional distribution provided by the software yields considerable insight into the multivariate shape.