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Statistics of orthogonal axial frames

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  • R. Arnold
  • P. E. Jupp

Abstract

An orthogonal axial frame is a set of orthonormal unit vectors which are known only up to sign. Such frames arise in crystallography and seismology and as principal axes of multivariate data or of some physical tensors. We develop methods for analysing data of this form. A test of uniformity is given. Parametric models for orthogonal axial frames are presented and tests of location are considered. A brief illustrative example involving earthquakes is given. Copyright 2013, Oxford University Press.

Suggested Citation

  • R. Arnold & P. E. Jupp, 2013. "Statistics of orthogonal axial frames," Biometrika, Biometrika Trust, vol. 100(3), pages 571-586.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:3:p:571-586
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    File URL: http://hdl.handle.net/10.1093/biomet/ast017
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    Citations

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    Cited by:

    1. Arnold, R. & Jupp, P.E. & Schaeben, H., 2018. "Statistics of ambiguous rotations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 73-85.
    2. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.
    3. Davy Paindaveine & Thomas Verdebout, 2017. "Detecting the Direction of a Signal on High-dimensional Spheres: Non-null and Le Cam Optimality Results," Working Papers ECARES ECARES 2017-40, ULB -- Universite Libre de Bruxelles.
    4. Bee, Marco & Benedetti, Roberto & Espa, Giuseppe, 2017. "Approximate maximum likelihood estimation of the Bingham distribution," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 84-96.
    5. Marco Bee & Roberto Benedetti & Giuseppe Espa, 2015. "Approximate likelihood inference for the Bingham distribution," DEM Working Papers 2015/02, Department of Economics and Management.
    6. Jupp, P.E. & Regoli, G. & Azzalini, A., 2016. "A general setting for symmetric distributions and their relationship to general distributions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 107-119.
    7. Iwashita, Toshiya & Klar, Bernhard & Amagai, Moe & Hashiguchi, Hiroki, 2017. "A test procedure for uniformity on the Stiefel manifold based on projection," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 89-96.

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