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Minimax properties of Fréchet means of discretely sampled curves

Bigot, Jérémie and Gendre, Xavier Minimax properties of Fréchet means of discretely sampled curves. (2013) The Annals of Statistics, 41 (2). 923-956. ISSN 0090-5364

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Official URL: http://dx.doi.org/10.1214/13-AOS1104

Abstract

We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of Fr´echet mean that is a generalization of the standard notion of averaging to non-Euclidean spaces. We derive a minimax rate for this estimation problem, and we show that our estimator achieves this optimal rate under the asymptotics where both the number of curves and the number of sampling points go to infinity.

Item Type:Article
Additional Information:Thanks to Institute of Mathematical Statistics (IMS) editor. The definitive version is available at http://imstat.org/aos/. The original PDF of the article can be found at The Annals of Statistics website:
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 > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (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:09 Sep 2013 10:13

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