Testing the equality of several multivariate normal mean vectors under heteroscedasticity: A fiducial approach and an approximate test

We consider the problem of testing the equality of several multivariate normal mean vectors under heteroscedasticity. We first construct a fiducial confidence region (FCR) for the differences between normal mean vectors and we then propose a fiducial test for comparing mean vectors by inverting the FCR. We also propose a simple approximate test that is based on a modification of the χ2 approximation. This simple test avoids the complications of simulation-based inference methods. We show that the proposed fiducial test has correct type one error rate asymptotically. We compare the proposed fiducial and approximate tests with the parametric bootstrap test in terms of controlling the type one error rate via an extensive simulation study. Our simulation results show that the proposed fiducial and approximate tests control the type one error rate, while there are cases that the parametric bootstrap test is out of control. We also discuss the power performance of the tests. Finally, we illustrate with a real example how our proposed methods are applicable in analyzing repeated measure designs including a single grouping variable.