Multivariate linear rank statistics for profile analysis

For some general multivariate linear models, linear rank statistics are used in conjunction with Roy's Union-Intersection Principle to develop some tests for inference on the parameter (vector) when they are subject to certain linear constraints. More powerful tests are designed by incorporating the a priori information on these constraints. Profile analysis is an important application of this type of hypothesis testing problem; it consists of a set of hypothesis testing problem for the p responses q-sample model, where it is a priori assumed that the response-sample interactions are null.