Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding and Measurement Errors
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Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounders or measurement errors. We focus on high-dimensional linear regression settings, where the measured covariates are affected by hidden confounding. We propose the Doubly Debiased Lasso estimator for single components of the regression coefficient vector. Our advocated method is novel as it simultaneously corrects both the bias due to estimating the 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, i.e. that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application.
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