Abstract: The inverse probability weighting (IPW) and doubly robust (DR) estimators are often used to estimate the average treatment effect (ATE), but are vulnerable to outliers. The IPW/DR median can be used to provide an outlier-resistant estimation of the ATE, but this resistance is limited, and is not sufficiently resistant to heavy contamination. We propose extending the IPW/DR estimators using density power weighting, which eliminates the effects of outliers almost completely. The resistance of the proposed estimators to outliers is evaluated using the unbiasedness of the estimating equations. Unlike the median-based methods, our estimators are resistant to outliers, even under heavy contamination. Interestingly, the naive extension of the DR estimator requires a bias correction to maintain its double robustness, even under the most tractable form of contamination. In addition, the proposed estimators are found to be highly resistant to outliers in more difficult settings in which the contamination ratio depends on the covariates. The resistance of our estimators to outliers from the viewpoint of the influence function is also favorable. We verify our theoretical results using Monte Carlo simulations and a real-data analysis. The proposed methods are shown to have greater resistance to outliers than the median-based methods do, and we estimate the potential mean with a smaller error than that of the median-based methods.

Key words and phrases: Causal inference, doubly robust, missing data, propensity score, robust statistics.