AN ADAPTABLE GENERALIZATION OF HOTELLING'S T2 TEST IN HIGH DIMENSION

• 成果类型: Article
• 署名作者: Li, Haoran; Aue, Alexander; Paul, Debashis; Peng, Jie; Wang, Pei
• 署名单位: University of California System; University of California Davis; Icahn School of Medicine at Mount Sinai
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1869
• 发表日期: 2020
• 页码: 1815-1847
• 关键词: 2-sample test; fewer observations; mean vector; eigenvalues

摘要

We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling's T-2. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the ridge-regularized Hotelling's T-2 is established and used to derive the cut-off values of the proposed test. Large sample properties are verified for a class of sub-Gaussian distributions. Through an extensive simulation study, the composite test is shown to compare favorably against a host of existing two-sample test procedures in a wide range of settings. The performance of the proposed test procedures is illustrated through an application to a breast cancer data set where the goal is to detect the pathways with different DNA copy number alterations across breast cancer subtypes.