An Improved Test for High-Dimensional Mean Vectors and Covariance Matrices Using Random Projection

This paper proposes an improved random-projection-based method for testing high-dimensional two-sample mean vectors and covariance matrices, building on the framework of . By incorporating training data to guide the construction of projection matrices toward the estimated mean difference, the proposed approach substantially enhances the power of the projected Hotelling’s $T^2$ statistic. We introduce three aggregation strategies—maximum, average, and percentile-based—to ensure stable performance across multiple projections. Extensive simulation studies illustrate that the proposed method performs favorably compared to a recent state-of-the-art technique, particularly in detecting sparse signals, while maintaining rigorous control of the Type-I error rate.