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Testing for Circular Reflective Symmetry about a Known Median Axis

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  • Arthur Pewsey

Abstract

Circular data arise in many contexts, a particularly rich source being animal orientation experiments. Often, in the analysis of such data, a fundamental question of scientific interest is whether the underlying distribution is reflectively symmetric about some specific axis. In this paper, the situation in which the axis of interest is known to be a median axis is considered and a simple, asymptotically distribution- free test for circular reflective symmetry against skew alternatives is developed. The results from a simulation study lead to a testing strategy incorporating the new test and the circular analogue of the modified runs test of Modarres & Gastwirth (1996). The application of the testing strategy is illustrated using circular data arising from two animal orientation experiments.

Suggested Citation

  • Arthur Pewsey, 2004. "Testing for Circular Reflective Symmetry about a Known Median Axis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(5), pages 575-585.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:5:p:575-585
    DOI: 10.1080/02664760410001681828
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    Citations

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    Cited by:

    1. Sara Salvador & Riccardo Gatto, 2022. "Bayesian tests of symmetry for the generalized Von Mises distribution," Computational Statistics, Springer, vol. 37(2), pages 947-974, April.
    2. Ley, Christophe & Verdebout, Thomas, 2017. "Skew-rotationally-symmetric distributions and related efficient inferential procedures," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 67-81.
    3. Oliveira, M. & Crujeiras, R.M. & Rodríguez-Casal, A., 2012. "A plug-in rule for bandwidth selection in circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3898-3908.
    4. Jose Ameijeiras-Alonso & Christophe Ley & Arthur Pewsey & Thomas Verdebout, 2021. "On optimal tests for circular reflective symmetry about an unknown central direction," Statistical Papers, Springer, vol. 62(4), pages 1651-1674, August.
    5. Christophe Ley & Thomas Verdebout, 2014. "Skew-rotsymmetric Distributions on Unit Spheres and Related Efficient Inferential Proceedures," Working Papers ECARES ECARES 2014-46, ULB -- Universite Libre de Bruxelles.
    6. Abe, Toshihiro & Pewsey, Arthur, 2011. "Symmetric circular models through duplication and cosine perturbation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3271-3282, December.

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