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dc.contributor.authorHoffmann, Marc
dc.contributor.authorRousseau, Judith
dc.contributor.authorSchmidt-Hieber, Johannes
dc.date.accessioned2017-03-09T16:26:55Z
dc.date.available2017-03-09T16:26:55Z
dc.date.issued2015
dc.identifier.issn0090-5364
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16328
dc.language.isoenen
dc.subjectBayesian nonparametricsen
dc.subjectminimax adaptive estimationen
dc.subjectposterior concentration ratesen
dc.subjectsup-normen
dc.subjectrates of convergenceen
dc.subject.ddc519en
dc.titleOn adaptive posterior concentration ratesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss under which the shrinking neighbourhood is considered, and an intrinsic pre-metric linked to frequentist separation rates. In the Gaussian white noise model, we construct feasible priors based on a spike and slab procedure reminiscent of wavelet thresholding that achieve adaptive rates of contraction under L2 or L∞ metrics when the underlying parameter belongs to a collection of Hölder balls and that moreover achieve our lower bound. We analyse the consequences in terms of asymptotic behaviour of posterior credible balls as well as frequentist minimax adaptive estimation. Our results are appended with an upper bound for the contraction rate under an arbitrary loss in a generic regular experiment. The upper bound is attained for certain sieve priors and enables to extend our results to density estimation.en
dc.relation.isversionofjnlnameAnnals of Statistics
dc.relation.isversionofjnlvol43en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages2259-2295en
dc.relation.isversionofdoi10.1214/15-AOS1341en
dc.identifier.urlsitehttps://arxiv.org/abs/1305.5270v3en
dc.relation.isversionofjnlpublisherIMSen
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.updated2017-03-09T15:25:00Z
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