Ridgelized Hotelling's T2 test on mean vectors of large dimension

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.