Adaptive robust estimation in sparse vector model
Résumé
For the sparse vector model, we consider estimation of the target vector, of its `2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet
"noise level – noise distribution – sparsity". We consider classes of noise distributions with polynomially and exponentially decreasing
tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax non-adaptive rates when the
triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can
also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an
adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the "nominal" distribution in advance
we assume that it belongs to some class of distributions.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...