Optimal designs in regression with correlated errors

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dc.contributor.authorDette, Holger
dc.contributor.authorPepelyshev, Andrey
dc.contributor.authorZhigljavsky, Anatoly
dc.date.accessioned2015-01-08T12:51:08Z
dc.date.available2015-01-08T12:51:08Z
dc.date.issued2015
dc.description.abstractThis paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimators achieve the same precision as the best linear unbiased estimator computed for the whole trajectory of the process. As a by-product we derive explicit expressions for the BLUE in the continuous time model and analytic expressions for the optimal designs in a wide class of regression models. We also demonstrate that for a finite number of observations the precision of the proposed procedure, which includes the estimator and design, is very close to the best achievable. The results are illustrated on a few numerical examples.en
dc.identifier.urihttp://hdl.handle.net/2003/33802
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-6714
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823;1/2015en
dc.subjectlinear regressionen
dc.subjectDoob representationen
dc.subjectGaussian processesen
dc.subjectBLUEen
dc.subjectoptimal designen
dc.subjectsigned measuresen
dc.subjectcorrelated observationsen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleOptimal designs in regression with correlated errorsen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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Sonderforschungsbereich (SFB) 823