Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem

A new test to the multivariate Behrens-Fisher problem is obtained by modifying Nel and Van der Merwe's (Comm. Statist. Theory Methods 15 (1986) 3719) test. The new test is affine invariant and it simplifies to the Welch's approximate solution to the univariate case. The merits of the new test and two existing invariant tests are evaluated using Monte Carlo method. Monte Carlo comparison shows that the new test is as powerful as the other two methods while controlling the sizes satisfactorily.