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2008 Adaptive estimation of linear functionals by model selection
Béatrice Laurent, Carenne Ludeña, Clémentine Prieur
Electron. J. Statist. 2: 993-1020 (2008). DOI: 10.1214/07-EJS127


We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with respect to the $\mathbb{L}_{p}$ loss. An application to the problem of estimating a signal or its rth derivative at a given point is developed and minimax rates are proved to hold uniformly over Besov balls. We also apply our non asymptotic oracle inequality to the estimation of the mean of the signal on an interval with length depending on the noise level. Simulations are included to illustrate the performances of the procedure for the estimation of a function at a given point. Our method provides a pointwise adaptive estimator.


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Béatrice Laurent. Carenne Ludeña. Clémentine Prieur. "Adaptive estimation of linear functionals by model selection." Electron. J. Statist. 2 993 - 1020, 2008.


Published: 2008
First available in Project Euclid: 27 October 2008

zbMATH: 1320.62074
MathSciNet: MR2448602
Digital Object Identifier: 10.1214/07-EJS127

Primary: 62G05 , 62G08

Keywords: adaptive estimation , linear functionals , Model selection , Nonparametric regression , Oracle inequalities , pointwise adaptive estimation , White noise model

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society


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