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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCarlier, Guillaume*
hal.structure.identifier
dc.contributor.authorChernozhukov, Victor*
hal.structure.identifier
dc.contributor.authorGalichon, Alfred*
dc.date.accessioned2014-04-28T14:38:26Z
dc.date.available2014-04-28T14:38:26Z
dc.date.issued2016
dc.identifier.issn0090-5364
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13155
dc.language.isoenen
dc.subjectBrenier
dc.subjectMonge-Kantorovich
dc.subjectvector conditional quantile function
dc.subjectVector quantile regression
dc.subject.ddc515en
dc.subject.classificationjelC21en
dc.subject.classificationjelC14en
dc.titleVector Quantile Regression: An optimal transport approach
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherSciences Po, Economics Departmen;France
dc.contributor.editoruniversityotherDepartment of Economics, MIT;Royaume-Uni
dc.description.abstractenWe propose a notion of conditional vector quantile function and a vectorquantile regression.A conditional vector quantile function (CVQF) of a random vectorY, taking valuesinRdgiven covariatesZ=z, taking values inRp, is a mapu7!QYjZ(u;z), which ismonotone, in the sense of being a gradient of a convex function, and such that given thatvectorUfollows a reference non-atomic distributionFU, for instance uniform distributionon a unit cube inRd, the random vectorQYjZ(U;z) has the conditional distribution ofYconditional onZ=z. Moreover, we have a strong representation,Y=QYjZ(U;Z) almostsurely, for some version ofU.The vector quantile regression (VQR) is a linear model for CVQF ofYgivenZ. Undercorrect speci cation, the notion produces strong representation,Y=(U)>f(Z), forf(Z) denoting a known set of transformations ofZ, whereu7!(u)>f(Z) is a monotonemap, the gradient of a convex function, and the quantile regression coe cientsu7!(u)have the interpretations analogous to that of the standard scalar quantile regression. Asf(Z) becomes a richer class of transformations ofZ, the model becomes nonparametric,as in series modelling. A key property of VQR is the embedding of the classical Monge-Kantorovich's optimal transportation problem at its core as a special case.In the classical case, whereYis scalar, VQR reduces to a version of the classical QR,and CVQF reduces to the scalar conditional quantile function. Several applications todiverse problems such as multiple Engel curve estimation, and measurement of nancialrisk, are considered.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameAnnals of Statistics
dc.relation.isversionofjnlvol44
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages1165-1192
dc.relation.isversionofdoi10.1214/15-AOS1401
dc.identifier.urlsitehttps://arxiv.org/abs/1406.4643v4
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-10-07T12:46:26Z
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