Maxiset comparisons of procedures, application to choosing priors in a Bayesian nonparametric setting - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2004

Maxiset comparisons of procedures, application to choosing priors in a Bayesian nonparametric setting

Résumé

In this paper our aim is to provide tools for easily calculating the maxisets of several procedures. Then we apply these results to perform a comparison between several Bayesian estimators in a non parametric setting. We obtain that many Bayesian rules can be described through a general behavior such as being shrinkage rules, limited, and/or elitist rules. This has consequences on their maxisets which happen to be automatically included in some Besov or weak Besov spaces, whereas other properties such as cautiousness imply that their maxiset conversely contains some of the spaces quoted above. We compare Bayesian rules taking into account the sparsity of the signal with priors which are combination of a Dirac with a standard distribution. We consider the case of Gaussian and heavy tail priors. We prove that the heavy tail assumption is not necessary to attain maxisets equivalent to the thresholding methods. Finally we provide methods using the tree structure of the dyadic aspect of the multiscale analysis, and related to Lepki's procedure, achieving strictly larger maxisets than those of thresholding methods.
Fichier principal
Vignette du fichier
PMA-931.pdf (831.34 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-00003028 , version 1 (08-10-2004)

Identifiants

  • HAL Id : hal-00003028 , version 1

Citer

Florent Autin, Dominique Picard, Vincent Rivoirard. Maxiset comparisons of procedures, application to choosing priors in a Bayesian nonparametric setting. 2004. ⟨hal-00003028⟩
306 Consultations
87 Téléchargements

Partager

Gmail Facebook X LinkedIn More