DOUBLY DEBIASED LASSO: HIGH-DIMENSIONAL INFERENCE UNDER HIDDEN CONFOUNDING

• 成果类型: Article
• 署名作者: Guo, Zijian; Cevid, Domagoj; Buhlmann, Peter
• 署名单位: Rutgers University System; Rutgers University New Brunswick; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2152
• 发表日期: 2022
• 页码: 1320-1347
• 关键词: covariance-matrix estimation; confidence-intervals; invalid instruments; gene-expression; selection; variables; regions; models; number; rates

摘要

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected by hidden confounding and propose the doubly debiased lasso estimator for individual components of the regression coefficient vector. Our advocated method simultaneously corrects both the bias due to estimation of high-dimensional parameters as well as the bias caused by the hidden confounding. We establish its asymptotic normality and also prove that it is efficient in the Gauss-Markov sense. The validity of our methodology relies on a dense confounding assumption, that is, that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application. The method is implemented by the DDL package available from CRAN.