TESTING HIGH-DIMENSIONAL REGRESSION COEFFICIENTS IN LINEAR MODELS
成果类型：
Article
署名作者：
Zhao, Alex; Li, Changcheng; Li, Runze; Zhang, Zhe
署名单位：
Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Dalian University of Technology
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/24-AOS2420
发表日期：
2024
页码：
2034-2058
关键词：
摘要：
This paper is concerned with statistical inference for regression coefficients in high-dimensional linear regression models. We propose a new method for testing the coefficient vector of the high-dimensional linear models, and establish the asymptotic normality of our proposed test statistic with the aid of the martingale central limit theorem. We derive the asymptotical relative efficiency (ARE) of the proposed test with respect to the test proshow that the ARE is always greater or equal to one under the local alternative studied in this paper. Our numerical studies imply that the proposed test with critical values derived from its asymptotical normal distribution may retain Type I error rate very well. Our numerical comparison demonstrates the proposed test performs better than existing ones in terms of powers. We further illustrate our proposed method with a real data example.