Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding

TL;DR

This paper introduces the Doubly Debiased Lasso estimator for high-dimensional linear regression, effectively correcting biases from estimation and hidden confounding, and demonstrates its asymptotic normality and efficiency.

Contribution

It proposes a novel estimator that addresses both estimation bias and hidden confounding bias in high-dimensional settings, with proven asymptotic properties.

Findings

Estimator achieves asymptotic normality.

Method is efficient in the Gauss-Markov sense.

Performs well in simulations and genomic data.

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.