References

ASYMPTOTIC APPROXIMATIONS FOR DISTRIBUTIONS OF TEST STATISTICS OF PROFILE HYPOTHESES FOR SEVERAL GROUPS UNDER NON-NORMALITY


[1] R. N. Bhattacharya and J. K. Ghosh, On the validity of the formal Edgeworth expansion, Ann. Statist. 6 (1978), 434-451.

[2] R. N. Bhattacharya and J. K. Ghosh, On moment conditions for valid formal Edgeworth expansions, J. Multivariate Anal. 27 (1988), 68-79.

[3] T. K. Chandra and J. K. Ghosh, Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables, Sankhyà A41 (1979), 22-47.

[4] Y. Fujikoshi, An asymptotic expansion for the distribution of Hotelling’s statistic under nonnormality, J. Multivariate Anal. 61 (1997), 187-193.

[5] Y. Fujikoshi, Asymptotic expansions for the distributions of multivariate basic statistics and one-way MANOVA tests under nonnormality, J. Statist. Plann. Inference 108 (2002), 263-282.

[6] S. W. Greenhouse and S. Geisser, On methods in the analysis of profile data, Psychometrika 24 (1959), 95-112.

[7] G. W. Hill and A. W. Davis, Generalized asymptotic expansions of Cornish-Fisher type, Ann. Math. Statist. 39 (1968), 1264-1273.

[8] T. Isogai, On measures of multivariate skewness and kurtosis, Math. Japon. 28 (1983), 251-261.

[9] K. Ito, Asymptotic formulae for the distribution of Hotelling’s generalized statistic, Ann. Math. Statist. 27 (1956), 1091-1105.

[10] K. Ito, Asymptotic formulae for the distribution of Hotelling’s generalized statistic, II, Ann. Math. Statist. 31 (1960), 1148-1153.

[11] T. Iwashita, Asymptotic null and non-null distribution of Hotelling’s statistic under the elliptical distribution, J. Statist. Plann. Inference 61 (1997), 85-104.

[12] Y. Kano, An asymptotic expansion of the distribution of Hotelling’s statistic under general distributions, Amer. J. Math. Management Sci. 15 (1995), 317-341.

[13] E. L. Kaplan, Tensor notation and the sampling cumulants of k-statistics, Biometrika 39 (1952), 319-323.

[14] K. V. Mardia, Measures of multivariate skewness and kurtosis with applications, Biometrika 57 (1970), 519-530.

[15] Y. Maruyama, Asymptotic expansions of the null distributions of some test statistics for profile analysis in general distributions, J. Statist. Plann. Inference 137 (2007), 506-526.

[16] D. F. Morrison, Multivariate Statistical Methods, (Fourth edition), Duxbury Press, (2005).

[17] C. R. Rao, Tests of significance in multivariate analysis, Biometrika 35 (1948), 58-79.

[18] G. A. F. Seber, A Matrix Handbook for Statisticians, John Wiley & Sons, New York, (2007).

[19] M. Siotani, On the distributions of the Hotelling’s statistics, Ann. Inst. Statist. Math. 8 (1956), 1-14.

[20] M. Siotani, An asymptotic expansion of the non-null distribution of Hotelling’s generalized statistic, Ann. Math. Statist. 42 (1971), 560-571.

[21] M. S. Srivastava, Profile analysis of several groups, Comm. Statist. Theory Methods 16 (1987), 909-926.

[22] H. Yanagihara, Asymptotic expansions of the null distributions of three test statistic in a nonnormal GMANOVA model, Hiroshima Math. J. 31 (2001), 213-262.