Outliers can severely distort causal effect estimation in observational studies, especially in small samples. We develop a doubly robust estimator of the ATE under a contaminated-data model that explicitly accommodates outliers. Robustness to outliers is delivered via a bounded-influence estimating equation for the outcome model and covariate balancing propensity scores (CBPS) for treatment assignment. To mitigate overfitting in high dimensions, we incorporate variable selection and unify all components within a penalized empirical likelihood framework. For further inference, we derive an optimal finite-sample confidence interval (CI) whose endpoints are invariant to outliers under the contaminated model. Across extensive simulations and two gene-expression applications (Golub; Khan pediatric tumor), the proposed ATE estimator and finite-sample CI outperform state-of-the-art competitors in bias, mean squared error, empirical coverage, and interval length over a wide range of contamination levels and sample sizes.
Lee et al. (Wed,) studied this question.