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dc.contributor.authorBlanchard, Gilles*
dc.contributor.authorHoffmann, Marc*
dc.contributor.authorReiß, Markus*
dc.date.accessioned2018-01-09T10:19:50Z
dc.date.available2018-01-09T10:19:50Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17254
dc.language.isoenen
dc.subjectLinear inverse problemsen
dc.subjectEarly stoppingen
dc.subjectDiscrepancy principleen
dc.subjectAdaptive estimationen
dc.subjectOracle inequalitiesen
dc.subject.ddc519en
dc.titleOptimal adaptation for early stopping in statistical inverse problemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenFor linear inverse problems Y = Aµ + ξ, it is classical to recover the unknown signal µ by iterative regularisation methods (µ (m) , m = 0, 1,. . .) so that the weak (or prediction) error A(µ (τ) − µ) 2 is controlled for some early stopping rule τ based on a discrepancy principle. In the context of statistical estimation with stochastic noise ξ, we study oracle adaptation in strong squared-error E µ (τ) − µ 2. We give precise lower bounds for estimation by early stopping. For a stopping rule based on the residual process oracle adaptation bounds are established for general linear iterative methods. The proofs use bias and variance transfer techniques from weak prediction error to strong L 2-error as well as convexity arguments and concentration bounds for the stochastic part. For Sobolev balls the adaptation bounds are shown to match the lower bounds. Adaptive early stopping for the Landweber and spectral cutoff methods are studied in further detail.en
dc.relation.isversionofjnlnameSIAM/ASA Journal on Uncertainty Quantification
dc.relation.isversionofjnlvol6
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages1043-1075
dc.relation.isversionofdoi10.1137/17M1154096
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01426253en
dc.relation.isversionofjnlpublisherSIAM
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2018-01-09T10:15:55Z
hal.person.labIds166564*
hal.person.labIds60*
hal.person.labIds477533*


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