dc.contributor.advisor Munk, Axel Prof. Dr. dc.contributor.author Guo, Qinghai dc.date.accessioned 2017-03-08T09:38:25Z dc.date.available 2017-03-08T09:38:25Z dc.date.issued 2017-03-08 dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-0023-3DCC-D dc.language.iso eng de dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject.ddc 510 de dc.title Multiscale Change-point Segmentation: Beyond Step Functions de dc.type doctoralThesis de dc.contributor.referee Munk, Axel Prof. Dr. dc.date.examination 2017-02-03 dc.description.abstracteng Many multiscale segmentation methods have been proven to work successfully for detecting multiple change-points, mainly because they provide faithful statistical statements, while at the same time allowing for efficient computation. Underpinning theory has been studied exclusively for models which assume that the signal is an unknown step function. However, when the signal is only approximately piecewise constant, which often occurs in practical applications, the behavior of multiscale segmentation methods is still not well studied. To narrow this gap, we investigate the asymptotic properties of a certain class of \emph{multiscale change-point segmentation} methods in a general nonparametric regression setting. de The main contribution of this work is the adaptation property of these methods over a wide range of function classes, although they are designed for step functions. On the one hand, this includes the optimal convergence rates (up to log-factor) for step functions with bounded or even increasing to infinite number of jumps.  On the other hand, for models beyond step functions, which are characterized by certain approximation spaces,  we show the optimal rates (up to log-factor) as well. This includes bounded variation functions and (piecewise) H\"{o}lder functions of smoothness order $0 < \alpha \leq 1$.  All results are formulated in terms of $L^p$-loss, $0 < p < \infty$, both almost surely and in expectation. In addition, we show that the convergence rates readily imply accuracy of feature detection, such as change-points, modes, troughs, etc. The practical performance is examined by various numerical simulations. dc.contributor.coReferee Krajina, Andrea Prof. Dr. dc.contributor.thirdReferee Huckemann, Stephan Prof. Dr. dc.contributor.thirdReferee Luke, Russell Prof. Dr. dc.contributor.thirdReferee Zhu, Chenchang Prof. Dr. dc.contributor.thirdReferee Habeck, Michael Dr. dc.subject.eng Adaptive estimation de dc.subject.eng approximation spaces de dc.subject.eng jump detection de dc.subject.eng model misspecification de dc.subject.eng multiscale inference de dc.subject.eng nonparametric regression de dc.subject.eng robustness de dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-0023-3DCC-D-8 dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.subject.gokfull Mathematik (PPN61756535X) de dc.identifier.ppn 881652482