Nonparametric Two-Sample Tests of High Dimensional Mean Vectors via Random Integration

• 成果类型: Article
• 署名作者: Jiang, Yunlu; Wang, Xueqin; Wen, Canhong; Jiang, Yukang; Zhang, Heping
• 署名单位: Jinan University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Sun Yat Sen University; Yale University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2141636
• 发表日期: 2024
• 页码: 701-714
• 关键词: breast-cancer; regions

摘要

Testing the equality of the means in two samples is a fundamental statistical inferential problem. Most of the existing methods are based on the sum-of-squares or supremum statistics. They are possibly powerful in some situations, but not in others, and they do not work in a unified way. Using random integration of the difference, we develop a framework that includes and extends many existing methods, especially in high-dimensional settings, without restricting the same covariance matrices or sparsity. Under a general multivariate model, we can derive the asymptotic properties of the proposed test statistic without specifying a relationship between the data dimension and sample size explicitly. Specifically, the new framework allows us to better understand the test's properties and select a powerful procedure accordingly. For example, we prove that our proposed test can achieve the power of 1 when nonzero signals in the true mean differences are weakly dense with nearly the same sign. In addition, we delineate the conditions under which the asymptotic relative Pitman efficiency of our proposed test to its competitor is greater than or equal to 1. Extensive numerical studies and a real data example demonstrate the potential of our proposed test. Supplementary materials for this article are available online.