Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices in high-dimensional settings

Abstract

In this paper, we discuss a two-way multivariate analysis of variance in high-dimensional settings. With a high-dimensional setting, we propose new approximate tests that work well under the following conditions: 1. The error vectors do not necessarily follow a multivariate normal distribution, 2. The cell sizes are unequal, 3. The cell covariance matrices are unequal, and 4. The dimension p is much larger than the total cell size n. The accuracy of the proposed tests with finite samples is shown through simulations for a variety of high-dimensional scenarios.