Open Access
2010 Sharp template estimation in a shifted curves model
Jérémie Bigot, Sébastien Gadat, Clément Marteau
Electron. J. Statist. 4: 994-1021 (2010). DOI: 10.1214/10-EJS576


This paper considers the problem of adaptive estimation of a template in a randomly shifted curve model. Using the Fourier transform of the data, we show that this problem can be transformed into a linear inverse problem with a random operator. Our aim is to approach the estimator that has the smallest risk on the true template over a finite set of linear estimators defined in the Fourier domain. Based on the principle of unbiased empirical risk minimization, we derive a nonasymptotic oracle inequality in the case where the law of the random shifts is known. This inequality can then be used to obtain adaptive results on Sobolev spaces as the number of observed curves tend to infinity. Some numerical experiments are given to illustrate the performances of our approach.


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Jérémie Bigot. Sébastien Gadat. Clément Marteau. "Sharp template estimation in a shifted curves model." Electron. J. Statist. 4 994 - 1021, 2010.


Published: 2010
First available in Project Euclid: 7 October 2010

zbMATH: 1329.62182
MathSciNet: MR2727451
Digital Object Identifier: 10.1214/10-EJS576

Primary: 62G07
Secondary: 41A29 , ‎42C40

Keywords: adaptive estimation , Curve alignment , inverse problem , Oracle inequality , random operator , Template estimation

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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