Optimal principal points estimators of multivariate distributions of location-scale and location-scale-rotation families

Shun Matsuura, Thaddeus Tarpey

研究成果: Article

抄録

A set of k points that optimally summarize a distribution is called a set of k-principal points, which is a generalization of the mean from one point to multiple points and is useful especially for multivariate distributions. This paper discusses the estimation of principal points of multivariate distributions. First, an optimal estimator of principal points is derived for multivariate distributions of location-scale families. In particular, an optimal principal points estimator of a multivariate normal distribution is shown to be obtained by using principal points of a scaled multivariate t-distribution. We also study the case of multivariate location-scale-rotation families. Numerical examples are presented to compare the optimal estimators with maximum likelihood estimators.

元の言語English
ページ(範囲)1-15
ページ数15
ジャーナルStatistical Papers
DOI
出版物ステータスAccepted/In press - 2018 3 20

Fingerprint

Principal Points
Multivariate Distribution
Estimator
Location-scale Family
Multivariate T-distribution
Multivariate Normal Distribution
Maximum Likelihood Estimator
Family
Multivariate distribution
Numerical Examples

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

これを引用

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abstract = "A set of k points that optimally summarize a distribution is called a set of k-principal points, which is a generalization of the mean from one point to multiple points and is useful especially for multivariate distributions. This paper discusses the estimation of principal points of multivariate distributions. First, an optimal estimator of principal points is derived for multivariate distributions of location-scale families. In particular, an optimal principal points estimator of a multivariate normal distribution is shown to be obtained by using principal points of a scaled multivariate t-distribution. We also study the case of multivariate location-scale-rotation families. Numerical examples are presented to compare the optimal estimators with maximum likelihood estimators.",
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AB - A set of k points that optimally summarize a distribution is called a set of k-principal points, which is a generalization of the mean from one point to multiple points and is useful especially for multivariate distributions. This paper discusses the estimation of principal points of multivariate distributions. First, an optimal estimator of principal points is derived for multivariate distributions of location-scale families. In particular, an optimal principal points estimator of a multivariate normal distribution is shown to be obtained by using principal points of a scaled multivariate t-distribution. We also study the case of multivariate location-scale-rotation families. Numerical examples are presented to compare the optimal estimators with maximum likelihood estimators.

KW - Location-scale family

KW - Location-scale-rotation family

KW - Multivariate normal distribution

KW - Multivariate t-distribution

KW - Principal points

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