In this paper, a ridgelized Hotelling’s T2 test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen et al. [A regularized Hotelling’s t2 test for pathway analysis in proteomic studies, J. Am. Stat. Assoc. 106(496) (2011) 1345–1360.] by relaxing their Gaussian assumption. This is achieved by establishing an exact four-moment theorem that is a simplified version of Tao and Vu’s [Random matrices: universality of local statistics of eigenvalues, Ann. Probab. 40(3) (2012) 1285–1315] work. Simulation results demonstrate the superiority of the proposed test over the traditional Hotelling’s T2 test and its several extensions in high-dimensional situations.

中文翻译：

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Ridgelized Hotelling 对大维平均向量的 T2 检验

在本文中，一个脊化的 Hotelling 的吨2检验是针对特定矩条件下大维平均向量的假设而开发的。它概括了 Chen 的主要结果等人. [正规化的霍特林吨2蛋白质组学研究中的通路分析测试，J.上午。统计。副教授。 106(496) (2011) 1345–1360.] 通过放宽他们的高斯假设。这是通过建立一个精确的四矩定理来实现的，该定理是 Tao 和 Vu 的 [随机矩阵：特征值的局部统计的普遍性，的简化版本，安。概率。 40(3) (2012) 1285–1315] 工作。仿真结果证明了所提出的测试优于传统的霍特林测试吨2test 及其在高维情况下的几个扩展。