Testing generalized linear models with high-dimensional nuisance parameters

• 成果类型: Article
• 署名作者: Chen, Jinsong; Li, Quefeng; Chen, Hua Yun
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of North Carolina; University of North Carolina Chapel Hill; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac021
• 发表日期: 2023
• 页码: 8399
• 关键词: CONFIDENCE-REGIONS; Lasso; estimators; inference

摘要

Generalized linear models often have high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional subvector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and are thus computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that, under certain regularity conditions, the Type-I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.