BARAUD , Yannick

Let $\pa{X_{t}}_{t\in T}$ be a family of real-valued centered random variables indexed by a countable set $T$. In the first part of this paper, we establish exponential bounds for the deviation probabilities of the supremum $Z=\sup_{t\in T}X_{t}$ by using the generic chaining device introduced in Talagrand (2005). Compared to concentration-type...

Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in the cases where G is a VC-subgraph or a VC-major class and it is of smaller order than those one could get...

We consider the problem of estimating the density $\Pi$ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when $n$ goes to infinity, uniform...

We observe a random measure N and aim at estimating its intensity s. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on...

The purpose of this paper is to pursue our study of ρ-estimators built from i.i.d. observations that we defined in Baraud et al. (2014). For a ρ-estimator based on some model S (which means that the estimator belongs to S) and a true distribution of the observations that also belongs to S, the risk (with squared Hellinger loss) is bounded by a...

Following Baraud, Birgé and Sart (2014), we pursue our attempt to design a universal and robust estimation method based on independent (but not necessarily i.i.d.) observations. Given such observations with an unknown joint distribution P and a dominated model for P, we build an estimator P based on and measure its risk by an Hellinger-type...

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We consider the problem of estimating a function s on [−1,1]k for large values of k by looking for some best approximation of s by composite functions of the form g ◦ u. Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions g, u and statistical...

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density estimation, they asymptotically coincide with the celebrated maximum likelihood estimators at least when the...

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....

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density estimation, they asymptotically coincide with the celebrated maximum likelihood estimators at least when the...

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in ℝn belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the tests achieve a prescribed power. In the functional regression model this general...

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in R n belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the tests achieve a prescribed power. In the functional regression model this general...

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...

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