A random decision for testing of the homogeneity of normal means against the tree order alternative

Abstract

A typical problem of interest is to compare the k + 1 normal means under the tree order restriction θ0 ≤ θi for i = 1, . . . , k. In this paper, we propose new multiple comparisons procedures for testing of the tree order constraint. New test procedures along with the corresponding simultaneous confidence intervals are motivated by some new estimation methods which are constructed based on a random decision and the Bayesian approach. Also, these procedures are developed for two-sided tree order alternatives. We compare the performance of the proposed methods with some existing test procedures, such as likelihood ratio test and some multiple comparisons tests for the tree order constraint. In some cases, the gains in power due to the proposed procedures are substantial. The results for two sided alternative are similar to the one-sided hypotheses and new procedures perform well for almost every configuration. We illustrate the efficiency of the proposed methods by analyzing of the two bioassay numerical examples.