Electronic Journal of Statistics

Adaptive estimation of linear functionals by model selection

Béatrice Laurent, Carenne Ludeña, and Clémentine Prieur

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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.

Article information

Electron. J. Statist., Volume 2 (2008), 993-1020.

First available in Project Euclid: 27 October 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G08: Nonparametric regression

Nonparametric regression white noise model adaptive estimation linear functionals model selection pointwise adaptive estimation oracle inequalities


Laurent, Béatrice; Ludeña, Carenne; Prieur, Clémentine. Adaptive estimation of linear functionals by model selection. Electron. J. Statist. 2 (2008), 993--1020. doi:10.1214/07-EJS127. https://projecteuclid.org/euclid.ejs/1225114040

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