Abouzar Bazyari

In the present paper, we are interested in testing the order restriction of mean vectors against all alternatives based on a sample from several p dimensional normal distributions. Here we consider the case when the covariance matrices are completely unknown but com- mon. We propose a test statistic and obtain the supremum of its upper tail probability under the null hypothesis. A reformulation of the test statistic is also provided based on the orthogonal projections on the closed convex cones to study its null distribution. Finally, a Monte Carlo simulation is presented to estimate its critical values.