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

Shun Matsuura () and Thaddeus Tarpey ()
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Shun Matsuura: Keio University
Thaddeus Tarpey: Wright State University

Statistical Papers, 2020, vol. 61, issue 4, No 13, 1629-1643

Abstract: 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.

Keywords: Location-scale family; Location-scale-rotation family; Multivariate normal distribution; Multivariate t-distribution; Principal points (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-018-0995-z

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