PAIRWISE MULTIPLE COMPARISONS OF MEAN VECTORS UNDER ELLIPTICAL POPULATIONS WITH UNEQUAL SAMPLE SIZES(Theory and Applications)

Simultaneous confidence intervals for pairwise multiple comparisons among mean vectors under elliptical populations are considered. The estimation of simultaneous confidence intervals is given by using the approximate upper percentiles of the T^2_<max> statistic based on Bonferroni's inequality. In order to obtain the upper percentiles of the T^2_<max> statistic, an asymptotic expansion for Hotelling's T^2-type statistic under elliptical distributions is derived by the perturbation method. The accuracy and conservativeness of the approximations are evaluated via a Monte Carlo simulation study.