Enhanced adaptive two-sample tests for high-dimensional data

The two-sample testing problem becomes particularly challenging in the so-called high-dimension, low sample size (HDLSS) setting. To address the unknown sparsity structure of the underlying signals, various adaptive procedures have been proposed, many of which rely on aggregating multiple tests across a range of tuning parameters. Li (Citation2021) introduced a simple, tuning-free adaptive method based on the order statistics of component-wise two-sample test statistics, demonstrating strong empirical performance in both sparse and dense signal regimes. However, we find that its performance degrades in the presence of strong correlations among components. In this paper, we identify the source of this limitation and propose a variance-reweighted modification to Li’s method. The proposed approach preserves the simplicity and tuning-free nature of the original one while offering improved power under strong correlations. Simulation studies and real data analyses show that our modified method compares favorably with the original one and other existing adaptive procedures across a wide range of settings, providing a practical and effective solution to the high-dimensional two-sample testing problem.