Penalized Empirical Likelihood for Doubly Robust Causal Inference under Contamination in High Dimensions

TL;DR

This paper introduces a robust, penalized empirical likelihood estimator for causal inference in high-dimensional, contaminated observational data, achieving consistency, robustness, and valid uncertainty quantification.

Contribution

It develops a novel doubly robust estimator combining bounded influence equations with covariate balancing, embedded in a penalized likelihood framework with nonconvex regularization, ensuring oracle properties.

Findings

Outperforms existing methods in bias and error metrics

Provides valid finite-sample confidence intervals

Maintains efficiency even without contamination

Abstract

We propose a doubly robust estimator for the average treatment effect in high dimensional low sample size observational studies, where contamination and model misspecification pose serious inferential challenges. The estimator combines bounded influence estimating equations for outcome modeling with covariate balancing propensity scores for treatment assignment, embedded within a penalized empirical likelihood framework using nonconvex regularization. It satisfies the oracle property by jointly achieving consistency under partial model correct ness, selection consistency, robustness to contamination, and asymptotic normality. For uncertainty quantification, we derive a finite sample confidence interval using cumulant generating functions and influence function corrections, avoiding reliance on asymptotic approximations. Simulation studies and applications to gene expression datasets (Golub and Khan) demonstrate superior performance in bias, error metrics, and interval calibration, highlighting the method robustness and inferential validity in HDLSS regimes. One notable aspect is that even in the absence of contamination, the proposed estimator and its confidence interval remain efficient compared to those of competing models.