Improved test statistics for multivariate regression

Edgeworth expansions to the null distributions of three classical test statistics in the multivariate regression model were derived by Rothenberg (University of California at Berkeley, Working Paper IP-225, 1977) and Phillips (Journal of the Japan Statistical Society, 1984, 14, 107–124) for the purpose of obtaining size-corrected critical values for such tests. We combine their results with the results of Cordeiro and Ferrari (Biometrika, 1991, 78, 573–582) to obtain corrections to be applied to the test statistics directly. Simulation results are also given.