Self-Consistent Patterns for Symmetric Multivariate Distributions
Document Type
Article
Publication Date
1998
Abstract
The set of k points that optimally represent a distribution in terms of mean squared error have been called principal points (Flury 1990). Principal points are a special case of self-consistent points. Any given set of k distinct points in R p induce a partition of R p into Voronoi regions or domains of attraction according to minimal distance. A set of k points are called self-consistent for a distribution if each point equals the conditional mean of the distribution over its respective Voronoi region. For symmetric multivariate distributions, sets of self-consistent points typically form symmetric patterns. This paper investigates the optimality of different symmetric patterns of self-consistent points for symmetric multivariate distributions and in particular for the bivariate normal distribution. These results are applied to the problem of estimating principal points.
Repository Citation
Tarpey, T.
(1998). Self-Consistent Patterns for Symmetric Multivariate Distributions. Journal of Classification, 15 (1), 57-79.
https://corescholar.libraries.wright.edu/math/181
DOI
10.1007/s003579900020
