  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.
