dc.contributor.advisor Huckemann, Stephan F. Prof. Dr. dc.contributor.author Telschow, Fabian Joachim Erich dc.date.accessioned 2016-11-04T09:37:31Z dc.date.available 2016-11-04T09:37:31Z dc.date.issued 2016-11-04 dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-002B-7C63-3 dc.language.iso eng de dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject.ddc 510 de dc.title Equivariant Functional Shape Analysis in SO(3) with Applications to Gait Analysis de dc.type doctoralThesis de dc.contributor.referee Huckemann, Stephan F. Prof. Dr. dc.date.examination 2016-09-16 dc.description.abstracteng In gait analysis of the knee joint the data is given by curves in the group of $3\times3$ rotation matrices. We introduce $\mathcal{S}$-equivariant functional models (viz., Gaussian perturbations of a center curve) and provide a uniform strong consistent estimator for the center curves. Here $\mathcal{S}$ is a certain Lie group, which models the effect of different marker placements and self-chosen walking speeds in real gait data. For this setup we provide estimators correcting for different marker placements and walking speeds and provide different statistical tools for example simultaneous confidence sets and permutation tests to analyze such data. The methods are applied to real gait data from an experiment studying the effect of short kneeling. de dc.contributor.coReferee Munk, Axel Prof. Dr. dc.subject.eng Lie groups de dc.subject.eng Gauss process de dc.subject.eng non-euclidean statistics de dc.subject.eng simultaneous confidence bands de dc.subject.eng perturbation models de dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-002B-7C63-3-5 dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.subject.gokfull Mathematics (PPN61756535X) de dc.identifier.ppn 871825414