Confidence bands for multivariate and time dependent inverse regression models

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dc.contributor.authorBissantz, Nicolai
dc.contributor.authorDette, Holger
dc.contributor.authorProksch, Katharina
dc.date.accessioned2012-06-18T12:35:19Z
dc.date.available2012-06-18T12:35:19Z
dc.date.issued2012-06-18
dc.description.abstractUniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for the supremum of a stationary Gaussian field over an increasing system of sets. As a particular application asymptotic confidence bands for a time dependent regression function ft(x) (x 2 Rd; t 2 R) in a convolution-type inverse regression model are obtained. To the best knowledge of the authors the results presented in this paper are the first which provide uniform confidence bands for multivariate nonparametric function estimation in inverse problems.en
dc.identifier.urihttp://hdl.handle.net/2003/29482
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-4811
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823;23/2012
dc.subjectconfidence bandsen
dc.subjectdeconvolutionen
dc.subjectinverse problemsen
dc.subjectmultivariate regressionen
dc.subjectnonparametric Regressionen
dc.subjectrates of convergenceen
dc.subjecttime dependent regression functionen
dc.subjectuniform convergenceen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleConfidence bands for multivariate and time dependent inverse regression modelsen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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