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

by Fabian Joachim Erich Telschow
Doctoral thesis
Date of Examination:2016-09-16
Date of issue:2016-11-04
Advisor:Prof. Dr. Stephan Huckemann
Referee:Prof. Dr. Stephan Huckemann
Referee:Prof. Dr. Axel Munk
Persistent Address: http://dx.doi.org/10.53846/goediss-5959

 

 

Files in this item

Name:Telschow_Dissertation_Publication.pdf
Size:2.05Mb
Format:PDF

The following license files are associated with this item:

Abstract

English

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.
Keywords: Lie groups; Gauss process; non-euclidean statistics; simultaneous confidence bands; perturbation models
 
Statistik