Show simple item record

dc.contributor.authorRousseau, Judith
dc.date.accessioned2010-04-16T08:59:43Z
dc.date.available2010-04-16T08:59:43Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3984
dc.language.isoenen
dc.subjectkernelen
dc.subjectBayesian nonparametricen
dc.subjectrates of convergenceen
dc.subjectmixtures of Betasen
dc.subjectadaptive estimationen
dc.subject.ddc519en
dc.subject.classificationjelC11en
dc.titleRates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the densityen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on [0, 1]. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while putting a prior on this scaling parameter. We prove that such Bayesian nonparametric models have good frequentist asymptotic properties. We determine the posterior rate of concentration around the true density and prove that it is the minimax rate of concentration when the true density belongs to a Hölder class with regularity β, for all positive β, leading to a minimax adaptive estimating procedure of the density. We also believe that the approximating results obtained on these mixtures of Beta densities can be of interest in a frequentist framework.en
dc.relation.isversionofjnlnameAnnals of Statistics
dc.relation.isversionofjnlvol38en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages146-180en
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/09-AOS703en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record