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Activity Number: 120 - SPEED: Nonparametric Statistics: Estimation, Testing, and Modeling
Type: Contributed
Date/Time: Monday, July 30, 2018 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #330822 Presentation
Title: A Bootstrap-Based Test for Distributional Symmetry in SO(3)
Author(s): Ulrike Genschel* and Daniel Nordman and Stephen Vardeman and Yalin Rao
Companies: Iowa State University and Iowa State University and Iowa State University and Iowa State University
Keywords: bootstrap; random rotations ; inference ; symmetry
Abstract:

Three-dimensional orientation data arise in various scientific studies, such as human kinematics, structural geology, and materials science.vIn many applications, it is of interest to investigate whether a random sample of orientations has symmetric distribution, whereby observations can be interpreted as directionally symmetric random perturbations of an underling mean-location rotation parameter.  For example, many common models for random rotations assume such distributional symmetry, but an approach to formally assess this broad modeling assumption is lacking for orientation data. In this talk, we provide a general characterization of distributional symmetry for random rotations, using an angle-axis representation of 3x3  rotations.  Under the assumption of symmetry, a random rotation is induced by three independent random variables, with two variables having  known (uniform-type) distributions. From this, we develop a novel test statistic for distribution asymmetry and investigate a convenient bootstrap procedure for approximating the complex sampling distribution of this statistic.


Authors who are presenting talks have a * after their name.

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