Estimating the Frèchet mean in Bookstein shape spaces

Kume, A. and Le, H.L (2000) Estimating the Frèchet mean in Bookstein shape spaces. Advances in Applied Probability, 32 (3). pp. 663-674. ISSN 0001-8678 . (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1239/aap/1013540237

Abstract

In [8], Le showed that procrustean mean shapes of samples are consistent estimates of Fréchet means for a class of probability measures in Kendall's shape spaces. In this paper, we investigate the analogous case in Bookstein's shape space for labelled triangles and propose an estimator that is easy to compute and is a consistent estimate of the Fréchet mean, with respect to sinh(δ/√2), of any probability measure for which such a mean exists. Furthermore, for a certain class of probability measures, this estimate also tends almost surely to the Fréchet mean calculated with respect to the Riemannian distance δ.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Alfred Kume
Date Deposited: 01 Jun 2009 07:26
Last Modified: 14 Jan 2010 14:32
Resource URI: http://kar.kent.ac.uk/id/eprint/8752 (The current URI for this page, for reference purposes)
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