TWO PRINCIPAL POINTS FOR MULTIVARIATE LOCATION MIXTURES OF SPHERICALLY SYMMETRIC DISTRIBUTIONS

Abstract

This article investigates two principal points of location mixtures of spherically symmetric distributions. We give a lemma which enables us to restrict the region to search principal points, and, with this lemma, prove a subspace theorem which states that there exist two principal points in the linear subspace spanned by the component means. We also give a sufficient condition for uniqueness of two principal points for two component cases. These results can be applied to a class of spherically symmetric distributions, which includes multivariate normal and t distributions.