Testing Homogeneity of a Parameter Matrix Some of the Rows of Which Are under Synchronized Order Restrictions

This research considers a multiple multivariate linear regression model with a parameter matrix some of the rows of which are constrained by synchronized order restrictions. The test on the homogeneity of the parameter matrix is considered. Under the assumption that the common variance covariance matrix is unknown, an ad-hoc test statistic is proposed by replacing the unknown covariance matrix with its estimate in a likelihood ratio test statistic. The deterministic and probabilistic properties of the test statistic are studied. It is shown that the family of ad hoc tests share the same alpha level critical values and follow the same distribution for computing their p values. A sufficient condition is established for other tests to enjoy these properties and to be more powerful. Two examples of such more powerful tests are provided.