Constructive Approximation

, Volume 31, Issue 2, pp 195–229 | Cite as

Maxisets for Model Selection

  • F. Autin
  • E. Le Pennec
  • J. M. Loubes
  • V. Rivoirard


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 give special attention to the issue of calculability and measure the induced loss of performance in terms of maxisets.


Approximation spaces Approximation theory Besov spaces Estimation Maxiset Model selection Rates of convergence 

Mathematics Subject Classification (2000)

62G05 62G20 41A25 42C40 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • F. Autin
    • 1
  • E. Le Pennec
    • 2
  • J. M. Loubes
    • 3
  • V. Rivoirard
    • 4
    • 5
  1. 1.Centre de Mathématiques et d’InformatiqueMarseille Cedex 13France
  2. 2.Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599Université Paris DiderotParisFrance
  3. 3.Institut de Mathématiques de Toulouse, Equipe de Probabilités et de StatistiqueUniversité de Toulouse Paul SabatierToulouseFrance
  4. 4.Laboratoire de Mathématiques, UMR 8628Université Paris-Sud.Orsay cedexFrance
  5. 5.Département de Mathématiques et Applications, UMR 8553Ecole Normale SupérieureParis Cedex 05France

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