Abstract
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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