A Novel Robust Test to Compare Covariance Matrices in High-Dimensional Data

Abstract

The comparison of covariance matrices is one of the most important assumptions in many multivariate hypothesis tests, such as Hotelling T2 and MANOVA. The sample covariance matrix, however, is singular in high-dimensional data when the variable number (p) is greater than the sample size (n). Therefore, its determinant is zero, and its inverse cannot be calculated. Although many studies addressing this problem are discussed in the Introduction Section, they have not focused on outliers in datasets. In this study, we propose a test statistic that can be used on high-dimensional datasets without being affected by outliers. There is no distributional assumption because our proposed test is permutational. We investigate the performance of the proposed test based on simulation studies and real example data. In all cases, our proposed test demonstrates good type-1 error control, power, and robustness. Additionally, we have constructed an R function and added it to the "MVTests" package. Therefore, our proposed test can be performed easily on real datasets.