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dc.contributor.authorBlanchard, Gilles
dc.contributor.authorHoffman, Marc
dc.contributor.authorReiß, Markus
dc.date.accessioned2019-04-16T12:17:40Z
dc.date.available2019-04-16T12:17:40Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18660
dc.language.isoenen
dc.subjector-acle inequalitiesen
dc.subjectLinear inverse problemsen
dc.subjecttruncated SVDen
dc.subjectspec-tral cut-offen
dc.subjectearly stoppingen
dc.subjectdiscrepancy principleen
dc.subjectadaptive estimationen
dc.subject.ddc519en
dc.titleEarly stopping for statistical inverse problems via truncated SVD estimationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider truncated SVD (or spectral cutoff , projection) es-timators for a prototypical statistical inverse problem in dimension D. Since calculating the singular value decomposition (SVD) only for the largest singular values is much less costly than the full SVD, our aim is to select a data-driven truncation level m ∈ {1,. .. , D} only based on the knowledge of the first m singular values and vectors. We analyse in detail whether sequential early stopping rules of this type can preserve statistical optimality. Information-constrained lower bounds and matching upper bounds for a residual based stopping rule are provided, which give a clear picture in which situation optimal sequential adaptation is feasible. Finally, a hybrid two-step approach is proposed which allows for classical oracle inequalities while considerably reducing numerical complexity.en
dc.relation.isversionofjnlnameElectronic journal of statistics
dc.relation.isversionofjnlvol12en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages3204-3231en
dc.relation.isversionofdoi10.1214/18-ejs1482en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01966326en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2019-03-26T14:34:38Z
hal.person.labIds27961
hal.person.labIds60
hal.person.labIds4560


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