Comparison of powers of some tests for testing homogeneity under order restrictions in multivariate normal means

In this paper attention is directed towards the construction of a reasonable test for testing the homogeneity of normal mean vectors against multi-variate isotonic alternatives. Since the covariate structure of the covariance matrices other than the independence with equal covariance matrices causes grave problems in computing the null distribution of the likelihood ratio test, we propose three possible test procedures, and investigate them through extensive simulations in the bivariate case.