B1765
Title: Bootstrap-based test of rotational symmetry in orientation data
Authors: Eva Biswas - Iowa State University (United States) [presenting]
Daniel Nordman - Iowa State University (United States)
Ulrike Genschel - Iowa State University (United States)
Abstract: Orientation data are of interest in a wide variety of fields, including human kinematics and materials science, where each observation can be represented by a $3\times 3$ rotation matrix $\mathbf{O}\in \mathcal{SO}(3)$, the set of orthogonal matrices with determinant 1. In many applications with orientation data, rotationally symmetric or isotropic distributions are commonly used for basic modelling purposes, which serve to conceptualize the variability in an orientation $\mathbf{O} = \mathbf{SR}$ due to directionally symmetric random perturbations $\mathbf{R}$ of an underlying location parameter $\mathbf{S} \in \mathcal{SO}(3)$. Rotational symmetry serves as an important, though simplifying, property for model-based inference about orientation data. A general bootstrap-based procedure for formally testing the property of rotational symmetry in orientation data is described. The bootstrap procedure re-creates data with rotational symmetry under the null hypothesis. Empirical processes induced by the orientation data have complex limits, which are not distribution-free and include further random components when parameter estimation is used. The resampling-based testing approach captures the true sampling distribution of the test statistics under rotational symmetry. The performance of the bootstrap-based testing method is evaluated through numerical studies, and the testing approach is illustrated with orientation data collected in texture analysis from materials science.
