Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems

dc.bibliographicCitation.firstPage2798eng
dc.bibliographicCitation.issue2eng
dc.bibliographicCitation.lastPage2841eng
dc.bibliographicCitation.volume14eng
dc.contributor.authorRastogi, Abhishake
dc.contributor.authorBlanchard, Gilles
dc.contributor.authorMathé, Peter
dc.date.accessioned2022-06-21T07:54:27Z
dc.date.available2022-06-21T07:54:27Z
dc.date.issued2020
dc.description.abstractWe study a non-linear statistical inverse problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization) approach to estimate the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the concept of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/9090
dc.identifier.urihttps://doi.org/10.34657/8128
dc.language.isoengeng
dc.publisherIthaca, NY : Cornell University Libraryeng
dc.relation.doihttps://doi.org/10.1214/20-EJS1735
dc.relation.essn1935-7524
dc.relation.ispartofseriesElectronic journal of statistics : EJS 14 (2020), Nr. 2eng
dc.rights.licenseCC BY 4.0 Unportedeng
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/eng
dc.subjectGeneral source conditioneng
dc.subjectMini-max convergence rateseng
dc.subjectReproducing kernel Hilbert spaceeng
dc.subjectStatistical inverse problemeng
dc.subjectTikhonov regular-izationeng
dc.subject.ddc310eng
dc.titleConvergence analysis of Tikhonov regularization for non-linear statistical inverse problemseng
dc.typearticleeng
dc.typeTexteng
dcterms.bibliographicCitation.journalTitleElectronic journal of statistics : EJSeng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeZeitschriftenartikeleng
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