Abstract

The estimation of causal effects based on the conditional average treatment effect (CATE) is usually vulnerable to outliers. However, to the best of our knowledge, outlier-resistant inference for the CATE has not been investigated in the literature. In this work, we propose an outlier-resistant estimation method for the CATE by incorporating M-estimation into the inverse propensity weighting (IPW) approach. The influence function and breakdown property are investigated to study the robustness of our method. In addition, we derive the asymptotic properties of the proposed estimator for inference purposes. The finite sample performance of the proposed estimator is evaluated via Monte Carlo experiments. The proposed method is compared with the IPW method and the augmented inverse probability weighting (AIPW) method, which do not account for outliers, as well as with DR-learner variants and machine-learning meta-learners, including the causal forest, X-learner, and R-learner. Finally, the proposed method is applied to the NHANES dataset to estimate the average effects of physical activity on albumin levels conditioned on age.

Key words and phrases: Conditional average treatment effect, Outlier-resistant estimators, Inverse probability weighting, M-estimator, Kernel regression

Information

Preprint No.SS-2026-0330
Manuscript IDSS-2026-0330
Complete AuthorsRan Mo, Honglang Wang
Corresponding AuthorsHonglang Wang
Emailshlwang@iu.edu

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Acknowledgments

This research was supported in part by the National Science Foundation under Grant DMS-2212928 and by Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute.

The study utilizes data from the National Health and Nutrition Examination Survey (NHANES), conducted by the National Center for Health Statistics, part of the Centers for Disease Control and Prevention (CDC).

Supplementary Materials

Technical proofs, detailed simulation results, and the full DR-learner and machine-learning meta-learner comparison studies summarised in Section 5.3, together with their implementation details, are provided in the supplementary material.

Supplementary materials are available for download.