An exact test for testing the equality of parameter matrices in two multivariate linear models

A method of testing the hypothesis of the kind H0:C′Φ1M=C′Φ2M in two independent multivariate linear models is presented using the concept of generalized p-values introduced by Tsui and Weerahandi [K.W. Tsui, S. Weerahandi, Generalized p-values in significance testing of hypothesis in the presence of nuisance parameters, J. Amer. Statist. Assoc. 84 (1989) 602–607] under the assumption of error matrix variate normality and heteroscedasticity. This method calculates the exact p-value in the generalized sense. Nel [D.G. Nel, Tests for equality of parameter matrices in two multivariate linear models, J. Multivariate Anal. 61 (1997) 29– 37] provided an approximate degrees of freedom test to test this hypothesis.