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Equivariant Functional Shape Analysis in SO(3) with Applications to Gait Analysis

dc.contributor.advisorHuckemann, Stephan Prof. Dr.
dc.contributor.authorTelschow, Fabian Joachim Erich
dc.titleEquivariant Functional Shape Analysis in SO(3) with Applications to Gait Analysisde
dc.contributor.refereeHuckemann, Stephan Prof. Dr.
dc.description.abstractengIn 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
dc.contributor.coRefereeMunk, Axel Prof. Dr.
dc.subject.engLie groupsde
dc.subject.engGauss processde
dc.subject.engnon-euclidean statisticsde
dc.subject.engsimultaneous confidence bandsde
dc.subject.engperturbation modelsde
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de

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