Modifications of the Rayleigh and Bingham Tests for Uniformity of Directions

Journal of Multivariate Analysis

Volumn 77, Issue 1, 2001, Pages 1-20

  Jupp, P E ^a  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

Complex projective space; Generalized Bartlett correction; Grassmann manifold; Rotation group; Sphere; Stiefel manifold; Uniform distribution

Indexed keywords

EID: 0041738902     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.2000.1922     Document Type: Article

References (19)

1. Barndorff-Nielsen O. E., Hall P. On the level-error after Bartlett adjustment of the likelihood ratio statistic. Biometrika. 75:1988;374-378.
2. Bingham C. An antipodally symmetric distribution on the sphere. Ann. Statist. 2:1974;1201-1225.
3. Chandra T. K., Mukerjee R. Bartlett-type modification for Rao's efficient score statistic. J. Multivariate Anal. 36:1991;103-112.
4. Chikuse Y. The matrix angular central Gaussian distribution. J. Multivariate Anal. 33:1990;265-274.
5. Chikuse Y., Watson G. S. Large sample asymptotic theory of tests for uniformity on the Grassmann manifold. J. Multivariate Anal. 54:1995;18-31.
6. -1. Biometrika. 78:1991;573-582.
7. Downs T. D. Orientation statistics. Biometrika. 59:1972;665-676.
8. Durand D., Greenwood J. A. Random unit vectors II: Usefulness of Gram-Charlier and related series in approximating distributions. Ann. Math. Statist. 28:1957;978-985.
9. James A. T. Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35:1964;475-501.
10. Kendall D. G. Shape manifolds, Procrustean metrics, and complex projective spaces. Bull. London Math. Soc. 16:1984;81-121.
11. Kent J. T. The complex Bingham distribution and shape analysis. J. Royal Statist. Soc. Ser. B. 56:1994;285-299.
12. Khatri C. G., Mardia K. V. The von Mises-Fisher matrix distribution in orientation statistics. J. Royal Statist. Soc. Ser. B. 39:1977;95-106.
13. Mardia K. V. Statistics of Directional Data. 1972;Academic Press, London.
14. Mardia K. V. Directional statistics and shape analysis. J. Appl. Statist. 26:1999;949-957.
15. Mardia K. V., Jupp P. E. Directional Statistics. 2000;Wiley, Chichester.
16. Mardia K. V., Khatri C. G. Uniform distribution on a Stiefel manifold. J. Multivariate Anal. 7:1977;468-473.
17. Pearson K. A Mathematical Theory of Random Migration. Drapers' Company Research Memoirs, Biometric Series III. 15:1906.
18. Prentice M. J. Orientation statistics without parametric assumptions. J. Royal Statist. Soc. Ser. B. 48:1986;214-222.
19. Wilkie D. Rayleigh test for randomness of circular data. Appl. Statist. 32:1983;311-312.