Abstract
SYNOPTIC ABSTRACTIn this article, conservative simultaneous confidence intervals for pairwise comparisons among mean vectors in multivariate normal distributions are considered. In order to give the simultaneous confidence intervals, we need the value of the upper 100α percentile of the T2max·p statistic. However, it is difficult to find the exact value. So, as an approximation procedure, Seo, Mano and Fujikoshi (1994) proposed the multivariate Tukey-Kramer procedure which is the multivariate version of Tukey-Kramer procedure (Tukey (1953); Kramer (1956, 1957)). Also, the multivariate version of the generalized Tukey conjecture has been affirmatively proved in the case of three correlated mean vectors by Seo, Mano and Fujikoshi (1994). In this article the affirmative proof of the multivariate generalized Tukey conjecture in the case of four mean vectors can be completed. Further, the upper bound for the conservativeness of the multivariate Tukey-Kramer procedure is also given. Finally, numerical results by Monte Carlo simulations and an example to illustrate the procedure are given.
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