Parallel principal axes are introduced and used to investigate the structure of multivariate distributions. In the class of elliptical distributions, it is shown that self-consistency of parallel principal axes characterizes normality. Parallel principal axes are used to illustrate the...

The paper shows that the fourth cumulant of a finite mixture distribution might be decomposed into the mean of the components’ fourth cumulants and the fourth cumulant of the components’ means, when the mixture’s components have the same second and third cumulants. Statistical applications...

We obtain random vectors with null third-order cumulants by projecting the data onto appropriate subspaces. Statistical applications include, but are not limited to, the robustification of Hotelling’s T2 test against nonnormality. Our approach only requires the existence of the third-order...