Asymptotic expansions for the distributions of multivariate basic statistics and one-way MANOVA tests under nonnormality

Journal of Statistical Planning and Inference

Volumn 108, Issue 1-2, 2002, Pages 263-282

  Fujikoshi, Yasunori ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Asymptotic expansion; Barlett correction; Nonnormality; One way MANOVA tests; Sample covariance matrix; Sample mean vector

Indexed keywords

EID: 0036839625     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00313-0     Document Type: Article

References (13)

1. Anderson, T.W., 1984. An Introduction to Multivariate Analysis, 2nd Edition. Wiley, New York.
2. Bhattacharya, R.N., Ghosh, J.K., 1978. On the validity of the formal Edgeworth expansion. Ann. Statist. 6, 434-451 (Corrigendum, ibid 8 (1980)).
3. Chandra, T.K., Ghosh, J.K., 1979. Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables. Sankhyā Ser. A 41, 22-47.
4. Fujikoshi, Y., 1977. An asymptotic expansion for the distributions of the latent roots of the Wishart matrix with multiple population roots. Ann. Inst. Statist. Math. 29, 379-387.
5. 2-statistic. J. Multivariate Anal. 61, 187-193.
6. Fujikoshi, Y., Ohmae, M., Yanagihara, H., 1999. Asymptotic approximations of the null distributions of one-way ANOVA test statistic under nonnormality. J. Japan Statist. Soc. 29, 147-161.
7. Hall, P., 1987. Edgeworth expansion for student's statistic under minimal moment conditions. Ann. Probab. 15, 920-931.
8. Hall, P., 1992. The Bootstrap and Edgeworth Expansions. Springer, New York.
9. Isogai, T., 1983. On measures of multivariate skewness and kurtosis. Math. Japon. 28, 251-261.
10. 2-statistic under general condition. Amer. J. Math. Management Sci. 15, 317-341.
11. Mardia, K.V., 1970. Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519-530.
12. Siotani, M., Hayakawa, T., Fujikoshi, Y., 1985. Modern Multivariate Statistical Analysis: a Graduate Course and Handbook. American Sciences Press, Columbus, Ohio.
13. Wakaki, H., 1997. Asymptotic expansion of the joint distribution of sample mean vector and sample covariance matrix from an elliptical population. Hiroshima Math. J. 27, 295-305.