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The inverse probability (IPW) and doubly robust (DR) estimators are oftenused to estimate the average causal effect (ATE), but are vulnerable tooutliers. The IPW/DR median can be used for outlier-resistant estimation of theATE, but the outlier resistance of the median is limited and it is notresistant enough for heavy contamination. We propose extensions of the IPW/DRestimators with density power weighting, which can eliminate the influence ofoutliers almost completely. The outlier resistance of the proposed estimatorsis evaluated through the unbiasedness of the estimating equations. Unlike themedian-based methods, our estimators are resistant to outliers even under heavycontamination. Interestingly, the naive extension of the DR estimator requiresbias correction to keep the double robustness even under the most tractableform of contamination. In addition, the proposed estimators are found to behighly resistant to outliers in more difficult settings where the contaminationratio depends on the covariates. The outlier resistance of our estimators fromthe viewpoint of the influence function is also favorable. Our theoreticalresults are verified via Monte Carlo simulations and real data analysis. Theproposed methods were found to have more outlier resistance than themedian-based methods and estimated the potential mean with a smaller error thanthe median-based methods.

Outlier-Resistant Estimators for Average Treatment Effect in Causal Inference