ON HIGH-DIMENSIONAL POISSON MODELS WITH MEASUREMENT ERROR: HYPOTHESIS TESTING FOR NONLINEAR NONCONVEX OPTIMIZATION

• 成果类型: Article
• 署名作者: Jiang, Fei; Zhou, Yeqing; Liu, Jianxuan; Ma, Yanyuan
• 署名单位: University of California System; University of California San Francisco; Tongji University; Syracuse University; 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: 10.1214/22-AOS2248
• 发表日期: 2023
• 页码: 233-259
• 关键词: CONFIDENCE-REGIONS; variable selection; general-theory; regularization; estimators; guarantees; regression; RECOVERY; noisy

摘要

We study estimation and testing in the Poisson regression model with noisy high-dimensional covariates, which has wide applications in analyz-ing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a nonconvex target function to minimize. Treating the high -dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L-1 and L-2 conver-gence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardi-nality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear func-tions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.