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dc.contributor.authorWellner, Jon
dc.contributor.authorBalabdaoui, Fadoua
dc.date.accessioned2010-07-22T15:08:56Z
dc.date.available2010-07-22T15:08:56Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4650
dc.language.isoenen
dc.subjectshape constraintsen
dc.subjectcompletely monotoneen
dc.subjectleast squaresen
dc.subjectmaximum likelihooden
dc.subjectminimax risken
dc.subjectmixture modelsen
dc.subjectmultiply monotoneen
dc.subjectnon-parametric estimationen
dc.subjectrates of convergenceen
dc.subject.ddc519en
dc.subject.classificationjelC14en
dc.titleEstimation of a k-monotone density: characterizations, consistency and minimax lower boundsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe classes of monotone or convex (and necessarily monotone) densities on inline image can be viewed as special cases of the classes of k-monotone densities on inline image. These classes bridge the gap between the classes of monotone (1-monotone) and convex decreasing (2-monotone) densities for which asymptotic results are known, and the class of completely monotone (∞-monotone) densities on inline image. In this paper we consider non-parametric maximum likelihood and least squares estimators of a k-monotone density g0. We prove existence of the estimators and give characterizations. We also establish consistency properties, and show that the estimators are splines of degree k−1 with simple knots. We further provide asymptotic minimax risk lower bounds for estimating the derivatives inline image, at a fixed point x0 under the assumption that inline image.
dc.relation.isversionofjnlnameStatistica Neerlandica
dc.relation.isversionofjnlvol64en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages45-70en
dc.relation.isversionofdoihttp://dx.doi.org/10.1111/j.1467-9574.2009.00438.xen
dc.identifier.urlsitehttp://arxiv.org/abs/math/0509080v1
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherWileyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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