Maxisets for μ-thresholding rules

In this paper, we study the performances of a large class of procedures, called mu-thresholding rules. At first, we exhibit the maximal spaces (or maxisets) where these rules attain given rates of convergence when considering the Besov-risk. Then, we point out a way to construct mu-thresholding rules for which the maxiset contains the hard thresholding rule's one. In particular, we prove that procedures which consist in thresholding coefficients by groups, as block thresholding rules or thresholding rules with tree structure, outperform in the maxiset sense procedures which consist in thresholding coefficients individually.