Abstract Testing the equality of two mean vectors is a classical problem in multivariate analysis. In this article, we consider the test in the high-dimensional setting. Existing tests often assume that the covariance matrix (or its inverse) of the underlying variables is sparse, which is rarely true in social science due to the existence of latent common factors. In the article, we introduce a maximum-type test statistic based on the factor-adjusted data. The factor-adjustment step increases the signal-to-noise ratio and thus results in more powerful test. We obtain the limiting null distribution of the maximum-type test statistic, which is the extreme value distribution of type I. To overcome the well-known slow convergence rate of the test statistic’s distribution to the limiting extreme value distribution, we also propose a multiplier bootstrap method to improve the finite-sample performance. In addition, a multiple testing procedure with false discovery rate (FDR) control is proposed for identifying specific locations that differ significantly between the two groups. Thorough numerical studies are conducted to show the superiority of the test over other state-of-the-art tests. The performance of the test is also assessed through a real stock market dataset.

中文翻译：

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高维二维样本均值向量检验，支持因子调整恢复

摘要 检验两个均值向量的相等性是多元分析中的一个经典问题。在本文中，我们考虑高维设置中的测试。现有的测试通常假设基础变量的协方差矩阵（或其逆矩阵）是稀疏的，由于存在潜在的公共因素，这在社会科学中很少为真。在文章中，我们介绍了基于因子调整数据的最大值类型检验统计量。因子调整步骤增加了信噪比，从而产生更强大的测试。我们得到最大型检验统计量的极限零分布，即类型I的极值分布。为了克服众所周知的检验统计量分布收敛速度慢的极限极值分布，我们还提出了一种乘法自举方法来提高有限样本性能。此外，还提出了具有错误发现率 (FDR) 控制的多重测试程序，用于识别两组之间存在显着差异的特定位置。进行了彻底的数值研究，以表明该测试优于其他最先进的测试。测试的性能也通过真实的股票市场数据集进行评估。