LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS

• 成果类型: Article
• 署名作者: Shi, Chengchun; Song, Rui; Chen, Zhao; Li, Runze
• 署名单位: North Carolina State University; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1761
• 发表日期: 2019
• 页码: 2671-2703
• 关键词: nonconcave penalized likelihood; variable selection; confidence-intervals; inference; regression; regions

摘要

This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are chi(2) distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow noncentral chi(2) distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to infinity at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.