Mixing Least-Squares Estimators when the Variance is Unknown

Christophe Giraud (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some cases the resulting estimator is a simple shrinkage estimator. We then apply this procedure in various statistical settings such as linear regression or adaptive estimation in Besov spaces. Our results provide non-asymptotic risk bounds for the Euclidean risk of the estimator.

Mots clés: Gibbs mixture; shrinkage estimator; oracle inequalities; adaptive estimation; linear regression

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Giraud. Mixing Least-Squares Estimators when the Variance is Unknown. 2007. ⟨hal-00184869⟩