Restricted one way analysis of variance using the empirical likelihood ratio test

Empirical likelihood (EL) ratio tests are developed for testing for or against the hypothesis that kk-population means μ1,μ2,…,μkμ1,μ2,…,μk are isotonic with respect to some quasi-order ⪯⪯ on {1,2,…,k}{1,2,…,k}. The null asymptotic distributions are derived and are shown to be of chi-bar squared type. The asymptotic power of the proposed test for testing for equality of these means against the order restriction is derived under contiguous alternatives and a simulation study is carried out to investigate the finite sample behaviors of this test. In addition, an adjusted EL test is used to improve the small size performance of our test and an example is also discussed to illustrate the theoretical results.