Principal points

This is the authors' abstract. We don't add key points for this paper.

The k principal points of a p-variate random variable X are defined as those points ξl,…ξk which minimize the expected squared distance of X from the nearest of the ξj. This paper presents results on the principal points of univariate symmetric distributions, the univariate and bivariate normal distribution, multivariate elliptical distributions, and multivariate distributions in general. In the cases of normal and elliptical distributions, the relationship between principal points and principal components is studied.