Maxisets for Model Selection
Statistics Theory
2008-12-16 v2 Statistics Theory
Abstract
We address the statistical issue of determining the maximal spaces (maxisets) where model selection procedures attain a given rate of convergence. By considering first general dictionaries, then orthonormal bases, we characterize these maxisets in terms of approximation spaces. These results are illustrated by classical choices of wavelet model collections. For each of them, the maxisets are described in terms of functional spaces. We take a special care of the issue of calculability and measure the induced loss of performance in terms of maxisets.
Cite
@article{arxiv.0802.4192,
title = {Maxisets for Model Selection},
author = {Florent Autin and Erwan Le Pennec and Jean-Michel Loubes and Vincent Rivoirard},
journal= {arXiv preprint arXiv:0802.4192},
year = {2008}
}