Estimating principal points of univariate distributions
The term 'principal points' originated in a problem of determining 'typical' heads for the design of protection masks, as described by Flury. Two principal points in the mask example correspond to a small and a large size. Principal points are cluster means for theoretical distributions, and sample cluster means from a k -means algorithm are non-parametric estimators of principal points. This paper demonstrates that maximum likelihood estimators and semi-parametric estimators based on symmetry constraints typically perform much better than the k -means estimators. Asymptotic results on the efficiency of these estimators of two principal points for four symmetric univariate distributions are given. Simulation results are provided to examine the performance of the estimators for finite sample sizes. Finally, the different estimators of two principal points are compared using the head dimension data for the design of protection masks.
Year of publication: |
1997
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Authors: | Tarpey, Thaddeus |
Published in: |
Journal of Applied Statistics. - Taylor & Francis Journals, ISSN 0266-4763. - Vol. 24.1997, 5, p. 499-512
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Publisher: |
Taylor & Francis Journals |
Saved in:
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