A Robust High-Dimensional MANOVA Test Based on Weighted MRCD Estimation

Abstract

Classical MANOVA procedures are not directly applicable in high-dimensional settings where the number of variables is comparable to, or exceeds, the sample size, and many existing high-dimensional MANOVA tests remain sensitive to outlying observations. This study proposes a weighted minimum regularized covariance determinant (MRCD)-based robust Wilks’ Lambda test for one-way high-dimensional MANOVA. The proposed method combines MRCD-based robust location and scatter estimation with a robust distance-based reweighting step and uses permutation calibration to obtain p-values. Through extensive Monte Carlo simulations, the method is evaluated in terms of Type-I error control, power, and robustness under structured contamination. Under clean data, the proposed test maintains empirical Type-I error near the nominal level, with only modest aggregate differences from Cheng-GM; Schott’s test can have higher power under weak signals. Under contaminated null scenarios where outliers create artificial group separation, the proposed method yields lower false-rejection rates than the competitors considered. A controlled sensitivity illustration using breast-cancer gene-expression data shows the same qualitative behavior after imposed contamination. The method is therefore positioned as a robustness-oriented option for contamination-prone high-dimensional MANOVA, at the cost of additional computation.