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A test of uniformity on shape spaces

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  • Chikuse, Y.
  • Jupp, P. E.

Abstract

A test of uniformity on the shape space [Sigma]mk is presented, together with modifications of the test statistic which bring its null distribution close to the large-sample asymptotic distribution. The asymptotic distribution under suitable local alternatives to uniformity is given. A family of distributions on [Sigma]mk is proposed, which is suitable for modelling shapes given by landmarks which are almost collinear.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:163-176
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    References listed on IDEAS

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    1. Mardia, K. V. & Khatri, C. G., 1977. "Uniform distribution on a Stiefel manifold," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 468-473, September.
    2. Chikuse, Y. & Watson, G. S., 1995. "Large Sample Asymptotic Theory of Tests for Uniformity on the Grassmann Manifold," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 18-31, July.
    3. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    4. Kenneth Jupp, 2000. "European Feudalism from its Emergence through its Decline," American Journal of Economics and Sociology, Wiley Blackwell, vol. 59(5), pages 27-45, November.
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    Cited by:

    1. 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.
    2. Huckemann, Stephan & Hotz, Thomas, 2009. "Principal component geodesics for planar shape spaces," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 699-714, April.
    3. Arnold, R. & Jupp, P.E. & Schaeben, H., 2018. "Statistics of ambiguous rotations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 73-85.

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