DOUBLY DEBIASED LASSO: HIGH-DIMENSIONAL INFERENCE UNDER HIDDEN CONFOUNDING.

Area of Science:

• Statistics
• Econometrics
• Genomics

Background:

• Observational data analysis is susceptible to hidden confounding, which can distort inferred relationships.
• High-dimensional linear regression models face challenges from both parameter estimation bias and unobserved confounding variables.

Purpose of the Study:

• To develop a robust statistical method for estimating regression coefficients in the presence of hidden confounding.
• To address the dual biases arising from high-dimensional parameter estimation and unobserved confounders.

Main Methods:

• Propose the Doubly Debiased Lasso estimator for individual regression coefficient components.
• Establish asymptotic normality and Gauss-Markov efficiency of the proposed estimator.
• Rely on a dense confounding assumption where confounders affect numerous covariates.

Main Results:

• The Doubly Debiased Lasso simultaneously corrects for estimation bias and hidden confounding bias.
• The method demonstrates theoretical efficiency in the Gauss-Markov sense.
• Validated through extensive simulations and a genomic data application.

Conclusions:

• The Doubly Debiased Lasso provides a valid approach for causal inference from observational data with hidden confounding.
• The dense confounding assumption is crucial for the methodology's effectiveness.
• The approach offers improved accuracy in high-dimensional regression settings affected by unobserved factors.