Statistical methods for random rotations

dc.contributor.advisor Ulrike Genschel Stanfill, Bryan
dc.contributor.department Statistics 2018-08-11T08:33:02.000 2020-06-30T02:51:58Z 2020-06-30T02:51:58Z Wed Jan 01 00:00:00 UTC 2014 2001-01-01 2014-01-01
dc.description.abstract <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>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 4767
dc.identifier.contextkey 5777461
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/13760
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 20:00:16 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Extrinsic estimators
dc.subject.keywords Influence fucntions
dc.subject.keywords Intrinsic estimators
dc.subject.keywords Robust statistics
dc.subject.keywords Rotation group
dc.title Statistical methods for random rotations
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca dissertation Doctor of Philosophy
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