Optimal estimators of principal points for minimizing expected mean squared distance

Shun Matsuura, Hiroshi Kurata, Thaddeus Tarpey

研究成果: Article査読

7 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)102-122
ページ数21
ジャーナルJournal of Statistical Planning and Inference
167
DOI
出版ステータスPublished - 2015 12 1

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性
  • 応用数学

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