A Bayes-motivated quadratic-form test for high-dimensional mean testing

Abstract We propose a two-sample mean test motivated by the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension p grows with the sample size n with a linear rate $$p/n \rightarrow c_1 \in (0, \infty )$$ . Under the Gaussian model, we establish the asymptotic normality of the test statistic and the asymptotic power. Through extensive simulations, we demonstrate that the proposed test performs competitively against several existing methods, particularly when the marginal variances of the individual features are heterogeneous and when the sample size is small. Additional non-Gaussian simulations provide empirical evidence of robustness to distributional misspecification. The proposed method not only effectively detects both sparse and non-sparse differences in mean vectors but also maintains a well-controlled type I error rate, even in small-sample scenarios. We also demonstrate the performance of our proposed test using the small round blue cell tumors (SRBCT) dataset.