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Modifications of the Rayleigh and Bingham Tests for Uniformity of Directions

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  • Jupp, P. E.

Abstract

The general machinery of Cordeiro and Ferrari (1991, Biometrika78, 573-582) and Chandra and Mukerjee (1991, J. Multivariate Anal.36, 103-112) provides modifications of score test statistics which bring the null distributions close to their large-sample asymptotic distributions. These modifications are calculated here for the Rayleigh and Bingham tests of uniformity on spheres of arbitrary dimension, Stiefel manifolds, rotation groups, Grassmann manifolds and complex projective spaces.

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  • Jupp, P. E., 2001. "Modifications of the Rayleigh and Bingham Tests for Uniformity of Directions," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 1-20, April.
    • Handle: RePEc:eee:jmvana:v:77:y:2001:i:1:p:1-20
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    References listed on IDEAS

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    1. D. Wilkie, 1983. "Rayleigh Test for Randomness of Circular Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(3), pages 311-312, November.
    2. Chikuse, Yasuko, 1990. "The matrix angular central Gaussian distribution," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 265-274, May.
    3. 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.
    4. 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.
    5. 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.
    6. Chandra, Tapas K. & Mukerjee, Rahul, 1991. "Bartlett-type modification for Rao's efficient score statistic," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 103-112, January.
    7. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
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    Cited by:

    1. Jupp, P.E., 2015. "Copulae on products of compact Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 92-98.
    2. Ebner, Bruno & Henze, Norbert & Yukich, Joseph E., 2018. "Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 231-242.
    3. Schott, James R., 2016. "On a robustness property of the Rayleigh and Bingham tests of uniformity," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 55-59.
    4. 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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