2008/02/28 by Florent Autin, Autin, Florent, Erwan Le Pennec +5
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Control Systems and Identification #FOS: Mathematics #Image and Signal Denoising Methods #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.0802.4192
openalex publication_date 2008/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.