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Pré-Publication, Document De Travail Année : 2010

Estimator selection in the Gaussian setting

Résumé

We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ the components of which are independent with a common variance that we assume to be unknown. Our estimation procedure is based on estimator selection. More precisely, we start with a collection $\FF$ of estimators of $f$ based on $Y$ and, with the same data $Y$, we aim at selecting an estimator among $\FF$ with the smallest Euclidean risk. We allow the cardinality of $\FF$ to be very large (possibly infinite) and also the dependency of the estimators with respect to the data to be possibly unknown. We establish a non-asymptotic risk bound for the selected estimator. When $\FF$ consists of linear estimators, we derive from this bound an oracle-type inequality. 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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Dates et versions

hal-00502156 , version 1 (13-07-2010)
hal-00502156 , version 2 (21-06-2011)

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Yannick Baraud, Christophe Giraud, Sylvie Huet. Estimator selection in the Gaussian setting. 2010. ⟨hal-00502156v1⟩
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