Abstract:
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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.
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