Tests for profile analysis in Behrens-Fisher problem

In this study, we consider profile analysis with unequal covariance matrices. We propose test statistics for testing parallelism, level and flatness hypotheses in a two-sample problem with unequal covariance matrices. We derive upper percentiles of these test statistics. Moreover, we propose modified Bartlett corrected statistics for three hypotheses. The approximate accuracy is evaluated via Monte Carlo simulations for some selected parameter values. Finally, a numerical example is presented to illustrate our proposed methods.