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A Test of Equality of Mean Vectors of Several Heteroscedastic Multivariate Populations

Journal of the Japan Statistical Society = 日本統計學會誌, v.37 no.2, 2007년, pp.253 - 283  

Kakizawa, Yoshihide (Faculty of Economics, Hokkaido University)

Abstract AI-Helper 아이콘AI-Helper

This paper deals with a test of equality of mean vectors of several heteroscedastic multivariate populations. We derive not only the asymptotic expansion up to N-1 of the nonnull distribution of James's (1954) statistic, but also those of two corrected statistics due to Cordeiro and Ferrari (1991) a...

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참고문헌 (24)

  1. 10.1007/978-3-0348-9254-4 (1) Bhattacharya, R. and Denker, M. (1990). Asymptotic Statistics , Birkhäuser-Verlag, Basel. 

  2. (2) Bhattacharya, R. N. and Ghosh, J. K. (1978). On the validity of the formal Edgeworth expansion, Ann. Statist. , 6 , 434–451. Correction: (1980). 8 , 1399. 

  3. (3) Bhattacharya, R. N. and Rao, R. R. (1976). Normal Approximation and Asymptotic Expansions , Wiley, New York. 

  4. (4) Chandra, T. K. and Ghosh, J. K. (1980). Valid asymptotic expansions for the likelihood ratio and other statistics under contiguous alternatives, Sankhya , 42 , 170–184. 

  5. (5) Chibisov, D. M. (1972). An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion, Theory Prob. Appl. , 17 , 620–630. 

  6. 10.1093/biomet/78.3.573 (6) Cordeiro, G. M. and Ferrari, S. L. P. (1991). A modified score test statistic having chi-squared distribution to order n −1 , Biometrika , 78 , 573–582. 

  7. 10.1214/aos/1176342465 (7) Eaton, M. L. and Perlman, M. D. (1973). The non-singularity of generalized sample covariance matrices, Ann. Statist. , 1 , 710–717. 

  8. (8) Fujikoshi, Y. (1997). An asymptotic expansion for the distribution of Hotelling's T 2 -statistic under nonnormality, J. Mult. Anal. , 61 , 187–193. 

  9. 10.1016/S0378-3758(02)00313-0 (9) Fujikoshi, Y. (2002a). Asymptotic expansions for the distributions of multivariate basic statistics and one-way MANOVA tests under nonnormality, J. Statist. Plan. Inf. , 108 , 263–282. 

  10. 10.1177/0008068320020501 (10) Fujikoshi, Y. (2002b). Some recent results on asymptotic expansions of multivariate test statistics for mean vectors under nonnormality, Calcutta Statist. Assoc. Bulletin , 52 , 1–46. 

  11. 10.1016/j.jmva.2005.03.012 (11) Gupta, A. K., Xu, J. and Fujikoshi, Y. (2006). An asymptotic expansion of the distribution of Rao's U -statistic under a general condition, J. Mult. Anal. , 97 , 492–513. 

  12. 10.1007/978-1-4612-4384-7 (12) Hall, P. (1992). The Bootstrap and Edgeworth Expansion , Springer, New York. 

  13. (13) Ito, K. (1969). On the effect of heteroscedasticity and nonnormality upon some multivariate test procedures, Multivariate Analysis II (ed. P. R. Krishnaiah), pp. 87–120, Academic Press, New York. 

  14. 10.1093/biomet/41.1-2.19 (14) James, G. S. (1954). Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown, Biometrika , 41 , 19–43. 

  15. 10.1093/biomet/83.4.923 (15) Kakizawa, Y. (1996). Higher order monotone Bartlett-type adjustment for some multivariate test statistics, Biometrika , 83 , 923–927. 

  16. (16) Kakizawa, Y. (2005). A comparison of local powers of a class of tests for multivariate linear hypothesis under general distributions. Discussion Paper Series A: No. 2005–142 & 162, 2006–168 and 2007–188, Faculty of Economics, Hokkaido University. 

  17. 10.55937/sut/1159987630 (17) Kakizawa, Y. (2006). Siotani's modified second approximation for multiple comparisons of mean vectors, SUT Journal of Mathematics , 42 , 59–96. 

  18. (18) Kakizawa, Y. and Iwashita, T. (2005). Hotelling's one-sample and two-sample T 2 tests and the multivariate Behrens-Fisher problem under nonnormality (this paper was accepted for publication in April 30, 2006), J. Statist. Plan. Inf. (to appear). 

  19. 10.1016/j.jmva.2007.07.005 (19) Kakizawa, Y. and Iwashita, T. (2008). A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions, doi:10.1016/j.jmva.2007.07.005, J. Mult. Anal. (to appear). 

  20. (20) Kano, Y. (1995). An asymptotic expansion of the distribution of Hotelling's T 2 -statistic under general distributions, Amer. J. Math. Management Sciences , 15 , 317–341. 

  21. 10.1017/S0266466600012974 (21) Magdalinos, M. A. (1992). Stochastic expansions and asymptotic approximations, Econometric Theory , 8 , 343–367. 

  22. (22) Wakaki, H., Yanagihara, H. and Fujikoshi, Y. (2002). Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality, Hiroshima Math. J. , 32 , 17–50. 

  23. (23) Yanagihara, H. (2000). Asymptotic expansion of the null distribution of one-way anova test statistic for heteroscedastic case under nonnormality, Commun. Statist. Theory Meth. , 29 , 463–476. 

  24. (24) Yanagihara, H. (2001). Asymptotic expansion of the null distribution of three test statistics in a nonnormal GMANOVA model, Hiroshima Math. J. , 31 , 213–262. 

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