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arXiv · 0802.4192

Maxisets for Model Selection

Florent Autin·Erwan Le Pennec·Jean-Michel Loubes·Vincent Rivoirard
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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.

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Florent Autin, Erwan Le Pennec, Jean-Michel Loubes, Vincent Rivoirard. 2008-12-16. Maxisets for Model Selection. https://arxiv.org/abs/0802.4192

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