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Estimator selection in the Gaussian setting

Abstract : We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection $\FF$ of estimators of $f$ based on $Y$ and, with the same data $Y$, aim at selecting an estimator among $\FF$ with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to $Y$ may be unknown. We establish a non-asymptotic risk bound for the selected estimator. As particular cases, our approach allows to handle the problems of aggregation and model selection as well as those of choosing a window and a kernel for estimating a regression function, or tuning the parameter involved in a penalized criterion. We also derive oracle-type inequalities when $\FF$ consists of linear estimators. For illustration, we carry out two simulation studies. One aims at comparing our procedure to cross-validation for choosing a tuning parameter. The other shows how to implement our approach to solve the problem of variable selection in practice.
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Contributor : Christophe Giraud Connect in order to contact the contributor
Submitted on : Tuesday, June 21, 2011 - 11:08:18 PM
Last modification on : Tuesday, September 7, 2021 - 3:32:56 PM
Long-term archiving on: : Thursday, September 22, 2011 - 2:27:47 AM


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  • HAL Id : hal-00502156, version 2
  • ARXIV : 1007.2096


Yannick Baraud, Christophe Giraud, Sylvie Huet. Estimator selection in the Gaussian setting. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2014. ⟨hal-00502156v2⟩



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