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Point de vue maxiset en estimation non paramétrique

Abstract : In the framework of a wavelet analysis, we study the statistical meaning of many classes of procedures. More precisely, we aim at investigating the maximal spaces (maxisets) where these procedures attain a given rate of convergence. The maxiset approach allows to bring theoretical explanations on some phenomena observed in the practical setting which are not explained by the minimax approach. Indeed, we show that data-driven thresholding rules outperform non random thresholding rules. Then, we prove that procedures which consist in thresholding coefficients by groups, as tree rules (close to Lepski's rule) or block thresholding rules, are often better in the maxiset sense than procedures which consist in thresholding coefficients individually. Otherwise, as many Bayesian rules built on heavy tailed densities, classical Bayesian rules built on Gaussian densities with large variance are proved to have maxisets which coincide with hard thresholding rules ones and to have very good numerical performances.
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Contributor : Florent Autin <>
Submitted on : Sunday, February 20, 2005 - 12:58:02 PM
Last modification on : Wednesday, December 9, 2020 - 3:06:03 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:31:24 PM


  • HAL Id : tel-00008542, version 1


Florent Autin. Point de vue maxiset en estimation non paramétrique. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2004. Français. ⟨tel-00008542⟩



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