Solution of Behrens-Fisher Problem For High-Dimensional Data and Comparison of Proposed Test Statistics

Comparison of multivariate mean of more than two groups is generally known as multivariate variance analysis (MANOVA) problem. However, classical test statistics used to solve MANOVA problems are highly affected by assumption violations. In addition, multivariate test statistics are insufficient in cases where the number of dependent variables is greater than the number of observations. This study aims to compare some proposed test statistics to determine whether mean vectors are equal in high-dimensional Behrens-Fisher problems. For this purpose, a simulation analysis was carried out for four different test statistics in cases where variance-covariance matrices are heterogeneous. Three different variance-covariance models were used in the study. In addition, different experimental conditions were taken into account for the number of dependent variables and the number of observations. The results of the study showed that the performances of the test statistics were generally comparable. However, it has been observed that the performance of test statistics varies according to experimental conditions.