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Adaptation in some linear inverse problems
Author(s) -
Johnstone Iain M.,
Paul Debashis
Publication year - 2014
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.54
Subject(s) - estimator , mathematics , gaussian , sequence (biology) , wavelet , mean squared error , range (aeronautics) , linear regression , inverse problem , mathematical optimization , inverse , basis (linear algebra) , algorithm , computer science , statistics , artificial intelligence , mathematical analysis , physics , materials science , geometry , quantum mechanics , biology , composite material , genetics
We consider the linear inverse problem of estimating an unknown signal f from noisy measurements on Kf where the linear operator K admits a wavelet–vaguelette decomposition. We formulate the problem in the Gaussian sequence model and propose estimation based on complexity penalized regression on a level‐by‐level basis. We adopt squared error loss and show that the estimator achieves exact rate‐adaptive optimality as f varies over a wide range of the Besov function classes. Copyright © 2014 John Wiley & Sons, Ltd.
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