We propose a method of testing a shift between mean vectors of two multivariate Gaussian random variables in a high-dimensional setting incorporating the possible dependency and allowing \(p > n\). This method is a combination of two well-known tests: the Hotelling test and the Simes test. The tests are integrated by sampling several dimensions at each iteration, testing each using the Hotelling test, and combining their results using the Simes test. We prove that this procedure is valid asymptotically. This procedure can be extended to handle non-equal covariance matrices by plugging in the appropriate extension of the Hotelling test. Using a simulation study, we show that the proposed test is advantageous over state-of-the-art tests in many scenarios and robust to violation of the Gaussian assumption.

我们提出了一种在高维设置中测试两个多元高斯随机变量的平均向量之间的偏移的方法，该方法包含可能的依赖性并允许\(p > n\)。这种方法是两个众所周知的测试的组合：Hotelling 测试和 Simes 测试。通过在每次迭代中对多个维度进行采样，使用 Hotelling 测试测试每个维度并使用 Simes 测试组合它们的结果来集成测试。我们证明这个过程是渐近有效的。通过插入 Hotelling 检验的适当扩展，可以扩展此过程以处理非等协方差矩阵。使用模拟研究，我们表明所提出的测试在许多情况下优于最先进的测试，并且对违反高斯假设具有鲁棒性。