z-logo
Premium
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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here