Inference for the Central Direction of Random Rotations in SO(3)

• Activity Number: 670
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Bryan Stanfill*+ and Ulrike Genschel and Heike Hofmann
• Companies: Iowa State University and Iowa State University and Iowa State University
• Keywords: Uniform-axis random spin distributions ; Stiefel manifold ; Spherical regression ; Quaternions ; Pivotal bootstrap

Abstract

Data as three-dimensional rotations have applications in computer science, kinematics and materials sciences, among other areas. Inference for the central orientation (mean) from a sample of such data is an important problem and has received increased attention in the literature, e.g. Rancourt et. al. (2000) and Bingham et. al. (2009). Currently, much of that attention has come from a parametric standpoint, which is only valid for large samples from a class of distributions that behaves normally in SO(3). In this paper we offer two non-parametric bootstrap procedures which achieve coverage rates closer to the nominal level under more general conditions. We also clarify an asymptotic result that motivates the parametric intervals already in the literature. Our methods are illustrated alongside our competitors' in a simulation study and data example.