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Median-based Splitting Rules for Causal Trees and Forests

Lennard Maßmann, Karolina Gliszczyńska-Schroeder

arXiv 7 Sep 2026 · Econometrics

arXiv:2609.07888 · PDF · Extracted main text

Abstract

Heavy-tailed and skewed outcomes are common in the randomized experiments and observational studies used to estimate heterogeneous treatment effects, yet the mean-squared-error criterion that guides splitting in honest causal trees is sensitive to the extreme values they generate. Building on the causal forest framework (Athey and Imbens, 2016; Wager and Athey, 2018), we introduce the Median Squared Deviation (MSD) criterion, which replaces the leafwise difference in means in the honest splitting objective with the Hodges--Lehmann location estimator while leaving honest leaf estimation and forest inference unchanged. Two further median-based rules, the Median Absolute Deviation (MAD) and the Least Median of Squares (LMS), serve as robust baselines. We evaluate the criteria in a simulation study covering precision, bias, and confidence interval coverage. MSD restricts its robustness to split selection and lowers the error of conditional average treatment effect estimates under heavy-tailed and skewed outcomes. Further, we re-visit two empirical applications: the first analyzes the electoral effects of a Mexican conditional cash transfer program on precinct-level observations, while the second application studies antiretroviral treatments in HIV-positive adults.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Leqi, Liu and Kennedy, Edward H (2022) Median Optimal Treatment Regimes1.00053100%
2Athey, Susan and Bickel, Peter J and Chen, Aiyou and Imbens, Guido W… (2023) Semiparametric estimation of treatment effects in randomised experiments0.96911591%
3De La O, Ana L (2013) Do Conditional Cash Transfers Affect Electoral Behavior? Evidence from a Randomized Experiment in Mexico0.9568388%
4Lin, Winston (2013) Agnostic notes on regression adjustments to experimental data: Reexamining Freedman’s critique0.9416383%
5Hammer, S. M. and Katzenstein, D. A. and Hughes, M. D. and Gundacker… (1996) A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 pe…0.9285380%
6Hastie, Trevor and Tibshirani, Robert and Friedman, Jerome (2009) The Elements of Statistical Learning0.92843100%
7Ghosh, Aditya and Deb, Nabarun and Karmakar, Bikram and Sen, Bodhisa… (2026) Robustness and efficiency of Rosenbaum’s rank-based estimator in randomized trials: a design-based perspective0.91613677%
8Wager, Stefan and Athey, Susan (2018) Estimation and Inference of Heterogeneous Treatment Effects using Random Forests0.87834868%
9Athey, Susan and Imbens, Guido (2016) Recursive partitioning for heterogeneous causal effects0.86534765%
10Richard A. J. Post and Edwin R. van den Heuvel (2025) Beyond conditional averages: Estimating the individual causal effect distribution0.81142100%

Showing the top 10 of 76 scored citations.