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Block‐threshold‐adapted Estimators via a Maxiset Approach
Author(s) -
Autin Florent,
Freyermuth JeanMarc,
Von Sachs Rainer
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12012
Subject(s) - estimator , thresholding , minimax , block (permutation group theory) , mathematics , separable space , adaptive estimator , minimax estimator , algorithm , computer science , statistics , mathematical optimization , artificial intelligence , combinatorics , minimum variance unbiased estimator , image (mathematics) , mathematical analysis
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.