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Article
Optimal Estimators of Principal Points for Minimizing Expected Mean Squared Distance
Journal of Statistical Planning and Inference
  • Shun Matsuura
  • Hiroshi Kurata
  • Thaddeus Tarpey, Wright State University - Main Campus
Document Type
Article
Publication Date
12-1-2015
Abstract
k-Principal points of a random variable are k points that minimize the mean squared distance (MSD) between the random variable and the nearest of the k points. This paper focuses on finding optimal estimators of principal points in terms of the expected mean squared distance (EMSD) between the random variable and the nearest principal point estimator. These estimators are compared with nonparametric and maximum likelihood estimators. It turns out that a minimum EMSD estimator of k-principal points of univariate normal distributions is determined by the k-principal points of the t-distribution with n+1 degrees of freedom, where n is the sample size. Extensions of the results to location-scale families, multivariate distributions, and principal surfaces are also discussed.
DOI
10.1016/j.jspi.2015.05.005
Citation Information
Shun Matsuura, Hiroshi Kurata and Thaddeus Tarpey. "Optimal Estimators of Principal Points for Minimizing Expected Mean Squared Distance" Journal of Statistical Planning and Inference Vol. 167 (2015) p. 102 - 122 ISSN: 03783758
Available at: http://works.bepress.com/thaddeus_tarpey/50/