Using Convex Cones in Testing one-sided Order Restriction of Mean Vectors

Using Convex Cones in Testing one-sided Order Restriction of Mean Vectors

In the present paper, we study the testing homogeneity of multivariate normal mean vectors against one sided restricted hypothesis based on the closed convex cones. We examine the test hypothesis when The covariance matrices are completely unknown but common. We firstly propose the test statistic and the critical values of test statistic estimate for different significance levels by using Monte Carlo simulation, then the test statistic is provided based on the orthogonal projections on the closed convex cones to study its null distribution