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dc.contributor.authorRousseau, Judith
dc.contributor.authorChopin, Nicolas
dc.contributor.authorLiseo, Brunero
dc.date.accessioned2010-07-23T14:57:24Z
dc.date.available2010-07-23T14:57:24Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4659
dc.language.isoenen
dc.subjectrates of convergenceen
dc.subjectGaussian long memory processesen
dc.subjectFEXP priorsen
dc.subjectconsistencyen
dc.subjectBayesian nonparametricen
dc.subject.ddc519en
dc.subject.classificationjelC14en
dc.subject.classificationjelC11en
dc.titleBayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian processen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenA stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density f(λ) can be written as f(λ)=|λ|−2dg(|λ|), where 0<d<1/2 (resp., −1/2<d<0), and g is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both d and g, under appropriate conditions on the prior distribution. We establish the rate of convergence for a general class of priors and apply our results to the family of fractionally exponential priors. Our approach is based on the true likelihood and does not resort to Whittle’s approximation.
dc.identifier.citationpages33en
dc.relation.isversionofjnlnameAnnals of Statistics
dc.relation.isversionofjnlvol40
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages964-995
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/11-AOS955SUPP
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00504969/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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