Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 853-870 |
| Number of pages | 18 |
| Journal | Statistical Papers |
| Volume | 55 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2014 |
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Keywords
- Allometric extension model
- Elliptically symmetric distribution
- Multivariate mixture distribution
- Principal components
- Principal points
- Principal subspace theorem
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Principal points for an allometric extension model. / Matsuura, Shun; Kurata, Hiroshi.
In: Statistical Papers, Vol. 55, No. 3, 2014, p. 853-870.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Principal points for an allometric extension model
AU - Matsuura, Shun
AU - Kurata, Hiroshi
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Allometric extension model
KW - Elliptically symmetric distribution
KW - Multivariate mixture distribution
KW - Principal components
KW - Principal points
KW - Principal subspace theorem
UR - http://www.scopus.com/inward/record.url?scp=84903907940&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903907940&partnerID=8YFLogxK
U2 - 10.1007/s00362-013-0532-z
DO - 10.1007/s00362-013-0532-z
M3 - Article
AN - SCOPUS:84903907940
VL - 55
SP - 853
EP - 870
JO - Statistical Papers
JF - Statistical Papers
SN - 0932-5026
IS - 3
ER -