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Statistical Multiscale Segmentation: Inference, Algorithms and Applications

dc.contributor.advisorMunk, Axel Prof. Dr.
dc.contributor.authorSieling, Hannes
dc.titleStatistical Multiscale Segmentation: Inference, Algorithms and Applicationsde
dc.contributor.refereeMunk, Axel Prof. Dr.
dc.description.abstractengThis thesis mainly concerns change-point models with independent observations from an exponential family with constant mean in between change-points. An inferential scheme for estimation and confidence statements based on a multiscale statistic is provided, which allows for efficient and accurate detection of multiple change-points. A universal bound for the asymptotic null-distribution of the considered multiscale statistic is derived. Based on this, the probability of over- and underestimation of change-points is bounded explicitly. From these bounds, model consistency is obtained and (asymptotically) honest confidence sets for the unknown change-point function and its change-points are constructed. The change-point locations are estimated at the minimax rate up to a logarithmic term. Moreover, the optimal detection rate of vanishing signals is attained. It is shown how dynamic programming can be used for efficient computation of estimators, confidence intervals and confidence bands for the change-point function. The performance and robustness of the approach are illustrated in various simulations and
dc.contributor.coRefereeSchuhmacher, Dominic Prof. Dr.
dc.subject.engmultiple testingde
dc.subject.engdynamic programmingde
dc.subject.engchange-point regressionde
dc.subject.engexponential familiesde
dc.subject.engmultiscale methodsde
dc.subject.enghonest confidence setsde
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de

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