Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding
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. 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, i.e. that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application.
Cite
@article{arxiv.2004.03758,
title = {Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding},
author = {Zijian Guo and Domagoj Ćevid and Peter Bühlmann},
journal= {arXiv preprint arXiv:2004.03758},
year = {2021}
}