Nonparametric monte carlo tests for multivariate distributions

Biometrika

Volumn 87, Issue 4, 2000, Pages 919-928

  Zhu, L I Xing ^a   Neuhaus, Georg ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Elliptical symmetry; Independent decomposition; Liouville dirichlet distribution; Monte carlo test; Reflection symmetry; Symmetric scale mixture

Indexed keywords

EID: 0013467628     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/87.4.919     Document Type: Article

References (22)

1. m. Ann. Inst. Statist. Math. 45, 787-800.
2. BARINGHAUS, L. (1991). Testing for spherical symmetry of a multivariate distribution. Ann. Statist. 19, 899-917.
3. BARNARD, G. A. (1963). Discussion of Professor Bartlett's paper. J. R. Statist. Soc. B 25, 294.
4. BERAN, R. (1979). Testing for ellipsoidal symmetry of a multivariate density. Ann. Statist. 7, 150-62.
5. BESAG, J. & DIGGLE, P. J. (1977). Simple Monte Carlo tests for spatial pattern. Appl. Statist. 26, 327-33.
6. CAMBANIS, S., HUANG, S. & SIMONS, G. (1981). On the theory of elliptically contoured distributions. J. Mult. Anal. 11, 368-85.
7. CAMBANIS, S., KEENER, R. & SIMONS, G. (1983). On a-symmetric distributions. J. Mult. Anal. 13, 313-33.
8. DIKS, C. & TONG, H. (1999). A test for symmetries of multivariate probability distributions. Biometrika 86, 605-14.
9. ENGEN, S. & LILLEGÅRD, M. (1997). Stochastic simulations conditioned on sufficient statistics. Biometrika 84, 235-40.
10. FANG, K. T., KOTZ, S. & NG, K. W. (1990). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.
11. GHOSH, S. & RUYMGAART, F. H. (1992). Applications of empirical characteristic functions in some multivariate problems. Can. J. Statist. 20, 429-40.
12. GUPTA, R. D. & RICHARD, D. ST. P. (1995). Multivariate Liouville distribution, IV. J. Mult. Anal. 54, 1-17.
13. GUTTMAN, I. & TIAO, G. C. (1965). The inverted Dirichlet distribution with applications. J. Am. Statist. Assoc. 60, 793-805.
14. HALL, P. & TITTERINGTON, D. M. (1989). The effect of simulation order on level accuracy and power of Monte Carlo tests. J. R. Statist. Soc. B 51, 459-67.
15. HEATHCOTE, C. R., RACHEV, S. T. & CHENG, B. (1995). Testing multivariate symmetry. J. Mult. Anal. 54, 91-112.
16. HENZE, N. & WAGNER, T. (1997). A new approach to the BHEP tests for multivariate normality. J. Mult. Anal. 62, 1-23.
17. HOPE, A. C. A. (1968). A simplified Monte Carlo test procedure. J. R. Statist. Soc. B 30, 582-98.
18. MARSHALL, A. W. & OLKIN, I. (1979). Inequalities: Theory of Majorization and Its Applications. New York: Academic Press.
19. NEUHAUS, G. & ZHU, L. X. (1998). Permutation tests for reflected symmetry. J. Mult. Anal. 67, 129-53.
20. OLKIN, I. & RUBIN, H. (1964). Multivariate Beta distributions and independence properties of the Wishart distributions. Ann. Math. Statist. 35, 261-9.
21. ROYSTON, J. P. (1983). Some techniques for assessing multivariate normality based on the Shapiro-Wilk W. Appl. Statist. 32, 121-33.
22. ZHU, L. X., FANG, K. T. & BHATTI, I. M. (1997). On estimated projection pursuit type Cramer-von Mises statistics. J. Mult. Anal. 63, 1-15.