MODIFIED MANOVA TESTS UNDER HETEROSCEDASTICITY

Abstract

In this thesis, we proposed modified MANOVA tests to the general linear hypothesis testing (GLHT) problem in heteroscedastic one-way and two-way MANOVA, respectively. All related tests under heteroscedastic MANOVA models can be unified under the common framework of the GLHT problem. The proposed modified MANOVA tests are shown to be invariant under affine-transformations, different choices of the contrast matrix used to define the same linear hypothesis, and different labeling schemes of the mean vectors. In addition, we made a significant improvement to some existing tests for heteroscedastic two-way MANOVA by making them affine-invariant and estimating the degrees of freedom of the random matrices involved in the test statistics by a better way. The performances of all the proposed tests are shown by simulation studies and real data examples. It was shown that the proposed tests outperform or are comparable with the existing tests in terms of size controlling and power.