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dc.contributor.authorKhazaei, Soleiman
dc.contributor.authorRousseau, Judith
dc.date.accessioned2010-07-20T12:55:02Z
dc.date.available2010-07-20T12:55:02Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4626
dc.language.isoenen
dc.subjectkernel mixtureen
dc.subjectk-monotone densityen
dc.subjectKullback Leibleren
dc.subjectentropyen
dc.subjectConsistencyen
dc.subjectNonparametric Bayesian inferenceen
dc.subject.ddc519en
dc.subject.classificationjelC14en
dc.subject.classificationjelC11en
dc.titleBayesian Nonparametric Inference of Decreasing Densitiesen
dc.typeCommunication / Conférence
dc.description.abstractenIn this paper we discuss consistency of the posterior distribution in cases where the Kullback-Leibler condition is not verified. This condition is stated as : for all $\epsilon > 0$ the prior probability of sets in the form $\{f ; KL(f0 , f ) \leq \epsilon\}$ where KL(f0 , f ) denotes the Kullback-Leibler divergence between the true density f0 of the observations and the density f , is positive. This condi- tion is in almost cases required to lead to weak consistency of the posterior distribution, and thus to lead also to strong consistency. However it is not a necessary condition. We therefore present a new condition to replace the Kullback-Leibler condition, which is usefull in cases such as the estimation of decreasing densities. We then study some specific families of priors adapted to the estimation of decreasing densities and provide posterior concentration rate for these priors, which is the same rate a the convergence rate of the maximum likelihood estimator. Some simulation results are provided.en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.conftitle42èmes Journées de Statistiqueen
dc.relation.confdate2010-05
dc.relation.confcityMarseilleen
dc.relation.confcountryFranceen


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