Principal points for an allometric extension model

Shun Matsuura, Hiroshi Kurata

研究成果: Article査読

8 被引用数 (Scopus)


A set of n-principal points of a p-dimensional distribution is an optimal n-point-approximation of the distribution in terms of a squared error loss. It is in general difficult to derive an explicit expression of principal points. Hence, we may have to search the whole space Rp for n-principal points. Many efforts have been devoted to establish results that specify a linear subspace in which principal points lie. However, the previous studies focused on elliptically symmetric distributions and location mixtures of spherically symmetric distributions, which may not be suitable to many practical situations. In this paper, we deal with a mixture of elliptically symmetric distributions that form an allometric extension model, which has been widely used in the context of principal component analysis. We give conditions under which principal points lie in the linear subspace spanned by the first several principal components.

ジャーナルStatistical Papers
出版ステータスPublished - 2014 7

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性


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