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Self-Consistent Patterns for Symmetric Multivariate Distributions
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  • Thaddeus Tarpey, Wright State University - Main Campus
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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.

Citation Information
Thaddeus Tarpey. "Self-Consistent Patterns for Symmetric Multivariate Distributions" Journal of Classification Vol. 15 Iss. 1 (1998) p. 57 - 79 ISSN: 0176-4268
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