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

Abstract

In this paper, Scheffe and Simplified Scheffe 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 Scheffe bounds are the same and they are shorter than Scheffe 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 Scheffe procedure for n ≥ n(p, k), otherwise Simplified Scheffe procedure is better. Finally, the authors find out that neither of Scheffe critical values nor Simplified Scheffe critical values are always larger than another through numerical calculation.