Electronic Journal of Statistics

Sharp template estimation in a shifted curves model

Jérémie Bigot, Sébastien Gadat, and Clément Marteau

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 994-1021.

Dates
First available in Project Euclid: 7 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1286455791

Digital Object Identifier
doi:10.1214/10-EJS576

Mathematical Reviews number (MathSciNet)
MR2727451

Zentralblatt MATH identifier
1329.62182

Subjects
Primary: 62G07: Density estimation
Secondary: 42C40: Wavelets and other special systems 41A29: Approximation with constraints

Keywords
Template estimation curve alignment inverse problem oracle inequality adaptive estimation random operator

Citation

Bigot, Jérémie; Gadat, Sébastien; Marteau, Clément. Sharp template estimation in a shifted curves model. Electron. J. Statist. 4 (2010), 994--1021. doi:10.1214/10-EJS576. https://projecteuclid.org/euclid.ejs/1286455791


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