Statistical methods for random rotations

<p>The analysis of orientation data is a growing field in statistics. Though the rotationally symmetric location model for orientation data is simple, statistical methods for estimation and inference for the location parameter, S are limited. In this dissertation we develop point estimation and confidence region methods for the central orientation.</p> <p>Both extrinsic and intrinsic approaches to estimating the central orientation S have been proposed in the literature, but no rigorous comparison of the approaches is available. In Chapter 2 we consider both intrinsic and extrinsic estimators of the central orientation and compare their statistical properties in a simulation study. In particular we consider the projected mean, geometric mean and geometric median. In addition we introduce the projected median as a novel robust estimator of the location parameter. The results of a simulation study suggest the projected median is the preferred estimator because of its low bias and mean square error.</p> <p>Non-parametric confidence regions for the central orientation have been proposed in the literature, but they have undesirable coverage rates for small samples. In Chapter 3 we propose a nonparametric pivotal bootstrap to calibrate confidence regions for the central orientation. We demonstrate the benefits of using calibrated confidence regions in a simulation study and prove the proposed bootstrap method is consistent.</p> <p>Robust statistical methods for estimating the central orientation has received very little attention. In Chapter 4 we explore the finite sample and asymptotic properties of the projected median. In particular we derive the asymptotic distribution of the projected median and show it is SB-robust for the Cayley and matrix Fisher distributions. Confidence regions for the central orientation S are proposed, which can be shown to have preferable finite sample coverage rates compared to those based on the projected mean.</p> <p>Finally the rotations package is developed in Chapter 5, which contains functions for the statistical analysis of rotation data in SO(3).</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

dissertation

Department dc:contributor.department

Department of Statistics (LAS)

Year dc:date.issued

2014

Author dc:creator

• Stanfill, Bryan

Advisor dc:contributor.advisor

• Ulrike Genschel

Language dc:language.iso

en

DOI

https://doi.org/10.31274/etd-180810-2216

Identifier

archive/lib.dr.iastate.edu/etd/13760/

OAI identifier oai:identifier

oai:dr.lib.iastate.edu:20.500.12876/27947