Optimal designs for comparing regression curves - dependence within and between groups

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dc.contributor.authorSchorning, Kirsten
dc.contributor.authorDette, Holger
dc.date.accessioned2021-01-12T20:42:25Z
dc.date.available2021-01-12T20:42:25Z
dc.date.issued2021
dc.description.abstractWe consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive effi- cient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous time model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous time model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.en
dc.identifier.urihttp://hdl.handle.net/2003/39974
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-21863
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;2/2021
dc.subjectoptimal designen
dc.subjectcomparison of curvesen
dc.subjectGaussian white noise modelen
dc.subjectcorrelated observationsen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.subject.rswkOptimale Versuchsplanungde
dc.subject.rswkGauss-Markov-Schätzungde
dc.titleOptimal designs for comparing regression curves - dependence within and between groupsen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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