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A permutation test for comparing rotational symmetry in three-dimensional rotation data sets

Author

Listed:
  • Melissa A. Bingham

    (University of Wisconsin-La Crosse)

  • Marissa L. Scray

    (University of Wisconsin-La Crosse)

Abstract

Although there have been fairly recent advances regarding inference for three-dimensional rotation data, there are still many areas of interest yet to be explored. One such area involves comparing the rotational symmetry of 3-D rotations. In this paper, nonparametric inference is used to test if F 1=F 2, where F i is the degree of rotational symmetry of distribution i, through a permutation test. The validity of the developed permutation test is examined through a simulation study and the test is applied to a small example in biomechanics.

Suggested Citation

  • Melissa A. Bingham & Marissa L. Scray, 2017. "A permutation test for comparing rotational symmetry in three-dimensional rotation data sets," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-8, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0075-2
    DOI: 10.1186/s40488-017-0075-2
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    References listed on IDEAS

    as
    1. D. Rancourt & L.‐P. Rivest & J. Asselin, 2000. "Using orientation statistics to investigate variations in human kinematics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 81-94.
    2. 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.
    3. Marissa D. Eckrote & Melissa A. Bingham, 2017. "A permutation test for the spread of three-dimensional rotation data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 553-560, July.
    4. Oualkacha, Karim & Rivest, Louis-Paul, 2009. "A new statistical model for random unit vectors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 70-80, January.
    5. Stanfill, Bryan & Genschel, Ulrike & Hofmann, Heike & Nordman, Dan, 2015. "Nonparametric confidence regions for the central orientation of random rotations," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 106-116.
    6. Rivest, Louis-Paul & Baillargeon, Sophie & Pierrynowski, Michael, 2008. "A Directional Model for the Estimation of the Rotation Axes of the Ankle Joint," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1060-1069.
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