%0 Journal Article
%T Block-threshold-adapted Estimators via a Maxiset Approach
%+ Institut de Mathématiques de Marseille (I2M)
%+ Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)
%A Autin, Florent
%A Freyermuth, Jean-Marc
%A von Sachs, Rainer
%< avec comité de lecture
%@ 0303-6898
%J Scandinavian Journal of Statistics
%I Wiley
%V 41
%N 1
%P 240-258
%8 2014-03
%D 2014
%R 10.1111/sjos.12012
%K Besov spaces
%K curve estimation
%K minimax and maxiset approaches
%K rate of convergence
%K thresholding methods
%K wavelet-based estimation
%Z Mathematics [math]/Statistics [math.ST]Journal articles
%X We study the maxiset performance of a large collection of block thresholding wavelet estimators, namely the horizontal 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.
%G English
%L hal-01286037
%U https://hal.science/hal-01286037
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-