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hal.structure.identifier
dc.contributor.authorvan der Pas, S.L.*
hal.structure.identifier
dc.contributor.authorSalomond, Jean-Bernard
HAL ID: 10173
*
hal.structure.identifier
dc.contributor.authorSchmidt-Hieber, Johannes*
dc.date.accessioned2017-03-15T15:09:10Z
dc.date.available2017-03-15T15:09:10Z
dc.date.issued2016
dc.identifier.issn1935-7524
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16362
dc.language.isoenen
dc.subjectsparsityen
dc.subjectnearly black vectorsen
dc.subjectnormal means problemen
dc.subjecthorseshoeen
dc.subjecthorseshoe+en
dc.subjectBayesian inferenceen
dc.subjectfrequentist Bayesen
dc.subjectposterior contractionen
dc.subjectshrinkage priorsen
dc.subject.ddc519en
dc.titleConditions for posterior contraction in the sparse normal means problemen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage priors has been proposed. Many of these shrinkage priors can be written as a scale mixture of normals, which makes them particularly easy to implement. We propose general conditions on the prior on the local variance in scale mixtures of normals, such that posterior contraction at the minimax rate is assured. The conditions require tails at least as heavy as Laplace, but not too heavy, and a large amount of mass around zero relative to the tails, more so as the sparsity increases. These conditions give some general guidelines for choosing a shrinkage prior for estimation under a nearly black sparsity assumption. We verify these conditions for the class of priors considered in [12], which includes the horseshoe and the normal-exponential gamma priors, and for the horseshoe+, the inverse-Gaussian prior, the normal-gamma prior, and the spike-and-slab Lasso, and thus extend the number of shrinkage priors which are known to lead to posterior contraction at the minimax estimation rate.en
dc.relation.isversionofjnlnameElectronic Journal of Statistics
dc.relation.isversionofjnlvol10en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages976-1000en
dc.relation.isversionofdoi10.1214/16-EJS1130en
dc.identifier.urlsitehttps://arxiv.org/abs/1510.02232v2en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-09T14:03:04Z
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