Projection Test for Mean Vector in High Dimensions

• 成果类型: Article
• 署名作者: Liu, Wanjun; Yu, Xiufan; Zhong, Wei; Li, Runze
• 署名单位: University of Notre Dame; Xiamen University; Xiamen University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2142592
• 发表日期: 2024
• 页码: 744-756
• 关键词: nonconcave penalized likelihood; 2-sample test

摘要

This article studies the projection test for high-dimensional mean vectors via optimal projection. The idea of projection test is to project high-dimensional data onto a space of low dimension such that traditional methods can be applied. We first propose a new estimation for the optimal projection direction by solving a constrained and regularized quadratic programming. Then two tests are constructed using the estimated optimal projection direction. The first one is based on a data-splitting procedure, which achieves an exact t-test under normality assumption. To mitigate the power loss due to data-splitting, we further propose an online framework, which iteratively updates the estimation of projection direction when new observations arrive. We show that this online-style projection test asymptotically converges to the standard normal distribution. Various simulation studies as well as a real data example show that the proposed online-style projection test retains the Type I error rate well and is more powerful than other existing tests. for this article are available online.