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Title: Doubly debiased lasso: High-dimensional inference under hidden confounding Authors:  Zijian Guo - Rutgers University (United States) [presenting]
Domagoj Cevid - ETH Zurich (Switzerland)
Abstract: 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 {\em Doubly Debiased Lasso} estimator for individual components of the regression coefficient vector. The advocated method simultaneously corrects both the bias due to the 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 this methodology relies on a dense confounding assumption, i.e. that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application.