This paper deals with aggregation of estimators in the context of regression with fixed design, with heteroscedastic and subgaussian noise. We relate the task of aggregating a finite family of affine estimators to the concentration of quadratic forms of the noise vector, and we derive sharp...

Discriminant analysis for two data sets in IRd with probability densities f and g can be based on the estimation of the set G = {x : f(x) Ï g(x)}. We consider applications where it is appropriate to assume that the region G has a smooth boundary. In particular, this assumption makes sense if...

on the basis of their commonly known strength levels, and privately observed strengthshocks

We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant covariates. The compound model is characterized by three...

We study the problem of detection of a p-dimensional sparse vector ofparameters in the linear regression model with Gaussian noise. We establishthe detection boundary, i.e., the necessary and sufficient conditions for thepossibility of successful detection as both the sample size n and the...

We consider the problem of estimating a sparse linear regression vector under a gaussiannoise model, for the purpose of both prediction and model selection. We assume that priorknowledge is available on the sparsity pattern, namely the set of variables is partitioned intoprescribed groups, only...