Construction and comparisons of simultaneous confidence intervals for the mean difference of multivariate normal distributions

In this paper, Scheffé and Simplified Scheffé simultaneous confidence intervals are first constructed for mean difference of several multivariate normal distributions. Then the authors theoretically prove that when there are only two populations, Bonferroni bounds and Simplified Scheffé bounds are the same and they are shorter than Scheffé bounds for p ≤ 10. In the case for 3 ≤ k ≤ 10 and 2 ≤ p ≤ 10, there exists n(p, k) such that Bonferroni method is better than Simplified Scheffé procedure for n ≥ n(p, k), otherwise Simplified Scheffé procedure is better. Finally, the authors find out that neither of Scheffé critical values nor Simplified Scheffé critical values are always larger than another through numerical calculation.