Constrained Simultaneous Confidence Intervals for Multiple Comparisons with the Best

Abstract

For comparing k treatment effects θ1,θ2,⋯θk, often the parameters of primary interest are θi−maxj≠iθj,i=1,⋯,k. In this article, we develop constrained 100P∗% two-sided simultaneous confidence intervals for θi−maxj≠iθj which we refer to as (constrained) MCB intervals. It turns out that the lower bounds of the intervals imply Indifference Zone selection inference, and the upper bounds of these intervals imply Subset Selection inference, each given at the same confidence level 100P∗% as MCB. We also extend our method to give 100P∗% simultaneous confidence intervals for θi−θ(i)(k−t),i=1,⋯,k, where θ(i)(k−t) is the tth largest among the θ's excluding θi.