IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v165y2018icp73-85.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1730194X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2017.10.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.
    2. Hielscher, Ralf & Lippert, Laura, 2021. "Locally isometric embeddings of quotients of the rotation group modulo finite symmetries," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Qiu, Yu & Nordman, Daniel J. & Vardeman, Stephen B., 2014. "One-sample Bayes inference for symmetric distributions of 3-D rotations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 520-529.
    3. 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.
    4. Bingham, Melissa A. & Nordman, Daniel J. & Vardeman, Stephen B., 2010. "Finite-sample investigation of likelihood and Bayes inference for the symmetric von Mises-Fisher distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1317-1327, May.
    5. Atsushi Inoue & Lutz Kilian, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," Working Papers 2030, Federal Reserve Bank of Dallas.
    6. Huckemann, Stephan & Hotz, Thomas, 2009. "Principal component geodesics for planar shape spaces," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 699-714, April.
    7. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    8. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.
    9. Marco Bee & Roberto Benedetti & Giuseppe Espa, 2015. "Approximate likelihood inference for the Bingham distribution," DEM Working Papers 2015/02, Department of Economics and Management.
    10. 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.
    11. 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.
    12. 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.
    13. Rau, Christian, 2013. "Bayes classifiers of three-dimensional rotations and the sphere with symmetries," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 930-935.
    14. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:73-85. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.