Outlier-Resistant Estimators for Average Treatment Effect in Causal Inference

Estimators for causal quantities sometimes suffer from outliers. We investigate outlier-resistant estimation for the average treatment effect (ATE) under challenging but realistic settings. We assume that the ratio of outliers is not necessarily small and that it can depend on covariates. We propose three types of estimators for the ATE, which combines the well-known inverse probability weighting (IPW)/doubly robust (DR) estimators with the density-power weight. Under heterogeneous contamination, our methods can reduce the bias caused by outliers. In particular, under homogeneous contamination, our estimators are approximately consistent with the true ATE. An influence-function-based analysis indicates that the adverse effect of outliers is negligible if the ratio of outliers is small even under heterogeneous contamination. We also derived the asymptotic properties of our estimators. We evaluated the performance of our estimators through Monte-Carlo simulations and real data analysis. The comparative methods, which estimate the median of the potential outcome, do not have enough outlier resistance. In experiments, our methods outperformed the comparative methods.