Online inference under over-parameterized models with hidden confounders

• 成果类型: Article; Early Access
• 署名作者: Chen, Shuyan; Feng, Xingdong; Ge, Yeheng; Li, Tao; Wu, Mengyun
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Shanghai University of Finance & Economics; Hong Kong Polytechnic University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag110
• 发表日期: 2026-06-29
• 关键词: dense models; High-dimensional Data; nonsparsity; Random Matrix Theory; Ridge Regression; False Discovery Rate; confidence-intervals; regression; Lasso

摘要

In this paper, we study online estimation and inference of regression coefficients in the presence of hidden confounders by leveraging over-parameterized models. Unlike existing offline approaches that rely on factor and sparse models, our closed-form estimator simultaneously removes hidden-confounder bias and is directly applicable to streaming data. Using tools from random matrix theory, we analyse phase transition phenomena in the variance of the coefficient estimator that arise as the sample size transitions from being smaller than to larger than the number of predictors. Notably, we show that adding more covariates only slightly affects the estimator's variance, mitigating concerns about variance inflation in over-parameterized settings. We validate the effectiveness of our method for both individual coefficient inference and multiple testing through simulations and applications to two real datasets.