Block‐threshold‐adapted Estimators via a Maxiset Approach
Florent Autin, Jean‐Marc Freyermuth, Rainer von Sachs · Scandinavian Journal of Statistics · 2013
ABSTRACT We study the maxiset performance of a large collection of block thresholding wavelet estimators, namely thehorizontal block thresholding family. We provide sufficient conditions on the choices of rates and threshold values to ensure that the involved adaptive estimators obtain large maxisets. Moreover, we prove that any estimator of such a family reconstructs the Besov balls with a near‐minimax optimal rate that can be faster than the one of any separable thresholding estimator. Then, we identify, in particular cases, the best estimator of such a family, that is, the one associated with the largest maxiset. As a particularity of this paper, we propose a refined approach that models method‐dependent threshold values. By a series of simulation studies, we confirm the good performance of the best estimator by comparing it with the other members of its family.