Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 62C10 Bayesian problems; characterization of Bayes procedures
- 62G05 Estimation
- 62G20 Asymptotic properties

**Résumé:** In this paper, our aim is to
estimate sparse sequences in the framework of the heteroscedastic white
noise model. To modelize sparsity, we consider a Bayesian model composed
of a mixture of a heavy-tailed density and a point mass at zero. To
evaluate the performance of the Bayes rules (the median or the mean of
the posterior distribution), we exploit an alternative to the
minimax setting developed in particular by Kerkyacharian and Picard: we
evaluate the maxisets for each of these estimators. Using this approach,
we compare the performance of Bayesian procedures with thresholding ones.
Furthermore, the maxisets obtained can be viewed as weighted versions of
weak $l_q$ spaces that naturally modelize sparsity. This remark leads us
to investigate the following problem: how can we choose the prior
parameters to build typical realizations of weak $l_q$ spaces ?

**Mots Clés:** *Bayes rules ; Bayesian model ; heteroscedastic white noise model ;
maxisets ; rate of convergence ; sparsity ; thresholding rules ; weak $l_q$ spaces*

**Date:** 2002-06-26

**Prépublication numéro:** *PMA-741*

**Pdf file : **PMA-741.pdf