Adaptive robust estimation in sparse vector model

摘要: For the sparse vector model, we consider estimation of target vector, its L2-norm and noise variance. We construct adaptive estimators establish optimal rates when adaptation is considered with respect to triplet "noise level - distribution sparsity". classes distributions polynomially exponentially decreasing tails as well case Gaussian noise. The obtained turn out be different from minimax non-adaptive known. A crucial issue ignorance Moreover, knowing or not can also influence rate. example, variance differ depending on whether sub-Gaussian without a precise knowledge distribution. Estimation in our setting viewed an variant robust scale contamination where instead fixing "nominal" advance, assume that it belongs some class distributions.