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Statistics of ambiguous rotations

Author

Listed:
  • Arnold, R.
  • Jupp, P.E.
  • Schaeben, H.

Abstract

The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analysing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.

Suggested Citation

  • Arnold, R. & Jupp, P.E. & Schaeben, H., 2018. "Statistics of ambiguous rotations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 73-85.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:73-85
    DOI: 10.1016/j.jmva.2017.10.007
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    References listed on IDEAS

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    1. Bingham, Melissa A. & Nordman, Daniel J. & Vardeman, Stephen B., 2009. "Modeling and Inference for Measured Crystal Orientations and a Tractable Class of Symmetric Distributions for Rotations in Three Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1385-1397.
    2. Chikuse, Y. & Jupp, P. E., 2004. "A test of uniformity on shape spaces," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 163-176, January.
    3. León, Carlos A. & Massé, Jean-Claude & Rivest, Louis-Paul, 2006. "A statistical model for random rotations," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 412-430, February.
    4. R. Arnold & P. E. Jupp, 2013. "Statistics of orthogonal axial frames," Biometrika, Biometrika Trust, vol. 100(3), pages 571-586.
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    Cited by:

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    2. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.

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