GIRAUD , Christophe

We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C , we introduce a collection of candidate graphs and...

Our aim in this paper is to investigate Gaussian graph estimation from a theoretical and non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and we focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C, we propose to introduce a collection of...

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...

We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C , we introduce a collection of candidate graphs and...

Let Y be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean μ of Y by model selection. More precisely, we start with a collection $\mathcal{S}=\{S_{m},m\in\mathcal{M}\}$ of linear subspaces of ℝn and associate to each of these the least-squares estimator of μ on Sm....

Let Y be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean μ of Y by model selection. More precisely, we start with a collection $\mathcal{S}=\{S_{m},m\in\mathcal{M}\}$ of linear subspaces of ℝn and associate to each of these the least-squares estimator of μ on Sm....

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...

We consider the problem of estimating the mean f of a Gaussian vector Y with independent components of common unknown variance σ 2 . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection F of estimators of f based on Y and, with the same data Y , aim at selecting an...

Let $Y$ be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean $\mu$ of $Y$ by model selection. More precisely, we start with a collection $\S=\ac{S_{m},\ m\in\M}$ of linear subspaces of $\R^{n}$ and associate to each of these the least-squares estimator of $\mu$ on...