Testing Homogeneity of Mean Vectors against ordered restriction in Multivariate Normal Distribution

This paper concerned with the testing of homogeneity of mean vectors against ordered restriction in multivariate normal distribution. Three different cases for covariance matrices are considered. First when covariance matrices are known, second when it is assume that covariance matrices have an unknown scale factor and third when the covariance matrices are completely unknown and equal. In two first cases the critical values of test statistic are computed for bivariate and trivariate normal distribution. The power and p-value of the test statistic are estimated by simulation method. When the covariance matrices are completely unknown and equal some tests are presented which the computation of those probabilities can be used as the upper bonds of p-values.