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On the consistency of Fréchet means in deformable models for curve and image analysis

Bigot, Jérémie and Charlier, Benjamin On the consistency of Fréchet means in deformable models for curve and image analysis. (2011) Electronic Journal of Statistics, 5. 1054-1089. ISSN 1935-7524

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Official URL: http://dx.doi.org/10.1214/11-EJS633

Abstract

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fr ́echet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points and the number J of observed curves (or images). Numerical experiments are given to illustrate the finite sample performances of the procedure.

Item Type:Article
Additional Information:Thanks to Institute of Mathematical Statistics editor. The definitive version is available at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ejs/1316092868
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Statistics:download
Deposited By: Jérémie Bigot
Deposited On:14 Mar 2013 16:27

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