Statistical Hypothesis Testing on Monotonic Mean Vectors in Multivariate Normal Distributions: Theories and Applications

Statistical hypothesis testing of ordered mean vectors Against all hypotheses on the means vector in multivariate normal distributions is considered. This problem of testing is investigated for known variance covariance matrices and unknown, but equal variance covariance matrices. When the covariance matrices are known, the test statistic is derived and upper bound of p-value is obtained. When the covariance matrices are completely unknown and equal, a test statistic based on the orthogonal projections on the closed convex cones is proposed and the null distribution of the test statistic derived. The critical values are estimated using simulation method. Also, the results are presented with application examples.