Principal points for an allometric extension model

Shun Matsuura () and Hiroshi Kurata

Statistical Papers, 2014, vol. 55, issue 3, 853-870

Abstract: A set of $$n$$ n -principal points of a $$p$$ p -dimensional distribution is an optimal $$n$$ 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 $$R^p$$ R p for $$n$$ 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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Allometric extension model; Elliptically symmetric distribution; Multivariate mixture distribution; Principal components; Principal points; Principal subspace theorem; 62E17; 62H25 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-013-0532-z (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:55:y:2014:i:3:p:853-870

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-013-0532-z

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().