On the computation of some properties of testing homogeneity of multivariate normal mean vectors against an order Restriction

Abstract

In the present article we are interested in presenting some properties of testing homogeneity of multivariate normal mean vectors against an order restriction for two cases, the covariance matrices are known, and the case that they have an unknown scale factor. This problem of testing with these two different cases was considered by Sasabuchi et al. (1983) and Kulatunga and Sasabuchi (1984). They only derived the test statistic and studied its null distribution. In this article, we obtain the critical values for the proposed test statistic by Kulatunga and Sasabuchi (1984) for the first case, at different significance levels for some of the two and three dimensional normal distributions. The power and p-value are computed using Monte Carlo simulation. We consider the case that covariance matrices have an unknown scale factor. In this case the specific conditions are given which under those the estimator of the unknown scale factor does not exist. Also we derive the unique test statistic. Some properties of this test, for instance, the critical values and power are computed by simulation study.