Outlier-Resistant Estimators for Average Treatment Effect in Causal Inference

TL;DR

This paper introduces density power weighted extensions of IPW and DR estimators that significantly improve outlier resistance in causal effect estimation, especially under heavy contamination, verified through simulations and real data.

Contribution

The paper proposes novel outlier-resistant extensions of IPW and DR estimators using density power weighting, enhancing robustness against heavy contamination.

Findings

Outlier resistance is improved with density power weighting.

Proposed estimators outperform median-based methods in heavy contamination.

Theoretical and empirical analyses confirm enhanced robustness.

Abstract

The inverse probability (IPW) and doubly robust (DR) estimators are often used to estimate the average causal effect (ATE), but are vulnerable to outliers. The IPW/DR median can be used for outlier-resistant estimation of the ATE, but the outlier resistance of the median is limited and it is not resistant enough for heavy contamination. We propose extensions of the IPW/DR estimators with density power weighting, which can eliminate the influence of outliers almost completely. The outlier resistance of the proposed estimators is evaluated through 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 bias correction to keep the 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 where the contamination ratio depends on the covariates. The outlier resistance of our estimators from the viewpoint of the influence function is also favorable. Our theoretical results are verified via Monte Carlo simulations and real data analysis. The proposed methods were found to have more outlier resistance than the median-based methods and estimated the potential mean with a smaller error than the median-based methods.