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dc.contributor.authorGassiat, Elisabeth
dc.contributor.authorRousseau, Judith
dc.contributor.authorVernet, Elodie
dc.date.accessioned2018-01-12T13:14:42Z
dc.date.available2018-01-12T13:14:42Z
dc.date.issued2018
dc.identifier.issn1935-7524
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17296
dc.language.isoenen
dc.subjectsemiparametric statistics
dc.subjectmixture models
dc.subjectefficiency
dc.subjectBernstein von Mises Theorem
dc.subject.ddc519en
dc.titleEfficient semiparametric estimation and model selection for multidimensional mixtures
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components which are independent given the population. We approximate the semiparametric model by projecting the conditional distributions on step functions associated to some partition. Our first main result is that if we refine the partition slowly enough, the associated sequence of maximum likelihood estimators of the weights is asymptotically efficient, and the posterior distribution of the weights, when using a Bayesian procedure, satisfies a semiparametric Bernstein von Mises theorem. We then propose a cross-validation like procedure to select the partition in a finite horizon. Our second main result is that the proposed procedure satisfies an oracle inequality. Numerical experiments on simulated data illustrate our theoretical results.
dc.relation.isversionofjnlnameElectronic Journal of Statistics
dc.relation.isversionofjnlvol12
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages703-740
dc.relation.isversionofdoi10.1214/17-EJS1387
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01345919
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-07-18T15:21:05Z


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