High-dimensional MANOVA under weak conditions

Recent results for comparison of high-dimensional mean vectors make assumptions that require weak dependence between the variables. These requirements fail to be satisfied, for example, by elliptically contoured distributions. In this paper, we relax the dependence conditions that seem to be the standard assumption in high-dimensional asymptotics. With the relaxed condition, the scope of applicability of the results broadens. In particular, an α-mixing type of dependence and general conditions on the variance of quadratic forms are covered. The problem is set up in a general and flexible form that extension of the results to general factorial design and profile analysis are formally illustrated. Simulation studies are used to evaluate the numerical performance of the results in practical scenarios. Data from an Electroencephalograph (EEG) experiment is analysed as an illustrative example.