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dc.contributor.authorCollier, Olivier
dc.contributor.authorComminges, Laëtitia
dc.contributor.authorTsybakov, Alexandre
dc.date.accessioned2018-09-04T11:34:26Z
dc.date.available2018-09-04T11:34:26Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17938
dc.language.isoenen
dc.subjectvariance estimationen
dc.subjectfunctional estimationen
dc.subjectsparsityen
dc.subjectrobust estimationen
dc.subjectadaptivityen
dc.subjectsub-Gaussian noiseen
dc.subject.ddc519en
dc.titleSome effects in adaptive robust estimation under sparsityen
dc.typeDocument de travail / Working paper
dc.description.abstractenAdaptive estimation in the sparse mean model and in sparse regression exhibits some interesting effects. This paper considers estimation of a sparse target vector, of its 2-norm and of the noise variance in the sparse linear model. We establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet noise level – noise distribution – sparsity". These rates turn out to be different from the minimax non-adaptive rates when the triplet is known. A crucial issue is the ignorance of the noise level. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise level can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise level 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. We also show that in the problem of estimation of a sparse vector under the 2-risk when the variance of the noise in unknown, the optimal rate depends dramatically on the design. In particular, for noise distributions with polynomial tails, the rate can range from sub-Gaussian to polynomial depending on the properties of the design.en
dc.identifier.citationpages21en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01707612en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2018-02
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2018-09-04T11:30:19Z
hal.person.labIds101
hal.person.labIds60
hal.person.labIds102$$$2579


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