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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorComminges, Laëtitia
HAL ID: 11573
hal.structure.identifierModélisation aléatoire de Paris X [MODAL'X]
dc.contributor.authorCollier, Olivier
hal.structure.identifierCentre de Recherche en Économie et Statistique [CREST]
dc.contributor.authorNdaoud, Mohamed
HAL ID: 7425
hal.structure.identifierEcole Nationale de la Statistique et de l'Analyse Economique [ENSAE]
dc.contributor.authorTsybakov, Alexandre
dc.date.accessioned2021-11-25T10:41:29Z
dc.date.available2021-11-25T10:41:29Z
dc.date.issued2021
dc.identifier.issn0090-5364
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22244
dc.language.isoenen
dc.subjectvariance estimationen
dc.subjectfunctional estimationen
dc.subjectsparsityen
dc.subjectrobust estimationen
dc.subjectadaptivityen
dc.subjectsub-Gaussian noiseen
dc.subject.ddc519en
dc.titleAdaptive robust estimation in sparse vector modelen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenFor the sparse vector model, we consider estimation of the target vector, of its ℓ2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet “noise level—noise distribution—sparsity.” We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax nonadaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the “nominal” distribution in advance we assume that it belongs to some class of distributions.en
dc.relation.isversionofjnlnameAnnals of Statistics
dc.relation.isversionofjnlvol49en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2021-06
dc.relation.isversionofjnlpages1347-1377en
dc.relation.isversionofdoi10.1214/20-AOS2002en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-11-25T10:38:42Z
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