Adaptive complexity regularization for linear inverse problems
Statistics Theory
2008-07-31 v1 Statistics Theory
Abstract
We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence without prior knowledge of the regularity of the function to be estimated. We provide for such estimators oracle inequalities and optimal rates of convergence. This penalized approach is applied to Tikhonov regularization and to regularization by projection.
Cite
@article{arxiv.0807.4859,
title = {Adaptive complexity regularization for linear inverse problems},
author = {Jean-Michel Loubes and Carenne Ludeña},
journal= {arXiv preprint arXiv:0807.4859},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-EJS115 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)