We propose a two-sample mean test based on 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 $p/n \to c_1 \in (0, \infty)$. 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. Furthermore, our test remains robust under distribution 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.

翻译：本文提出了一种基于无信息先验贝叶斯因子的两样本均值检验方法，专门针对维度$p$与样本量$n$以线性速率$p/n \to c_1 \in (0, \infty)$同步增长的场景。我们建立了检验统计量的渐近正态性及渐近功效。通过大量仿真实验证明，该检验方法在多个现有方法中具有竞争力，尤其当各特征边际方差存在异质性以及样本量较小时表现突出。此外，我们的检验在模型设定错误下仍保持稳健性。所提方法不仅能有效检测均值向量中的稀疏与非稀疏差异，而且即使在样本量较小的场景下也能良好控制第一类错误率。我们同时利用小圆蓝细胞肿瘤(SRBCT)数据集展示了本检验方法的性能表现。