Principal points of a multivariate mixture distribution

JOURNAL OF MULTIVARIATE ANALYSIS

卷:102

Article

Matsuura, Shun¹  Kurata, Hiroshi² 

[1] Aoyama Gakuin Univ, Coll Sci & Engn, Chuo Ku, Sagamihara, Kanagawa 2525258, Japan

[2] Univ Tokyo, Grad Sch Arts & Sci, Meguro Ku, Tokyo 1538902, Japan

关键词: Location mixture;    Mean squared distance;    Principal points;    Self-consistency;    Spherically symmetric distribution;   

DOI  :  10.1016/j.jmva.2010.08.009

来源: Elsevier

【 摘 要 】

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance It provides an optimal n-point-approximation of the distribution However it is in general difficult to find a set of principal points of a multivariate distribution Tarpey et al [T Tarpey L Li B Flury Principal points and self-consistent points of elliptical distributions Ann Statist 23 (1995) 103-112] established a theorem which states that any set of n-principal points of an elliptically symmetric distribution is in the linear subspace spanned by some principal eigenvectors of the covariance matrix This theorem called a principal subspace theorem is a strong tool for the calculation of principal points In practice we often come across distributions consisting of several subgroups Hence it is of Interest to know whether the principal subspace theorem remains valid even under such complex distributions In this paper we define a multivariate location mixture model A theorem is established that clarifies a linear subspace in which n-principal points exist (C) 2010 Elsevier Inc All rights reserved

【 授权许可】

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