Median-based splitting rules for the causal tree

We investigate the impact of median-based splitting rules on the performance of causal trees for treatment effect estimation in high-dimensional settings. Building on the causal forest framework, we introduce three novel splitting rules that partially rely on the Hodges-Lehmann estimator and the Wilcoxon Rank Sum statistic and serve as alternatives to conventional mean-based criteria: Median Absolute Deviation (MAD), Median Squared Deviation (MSD), and Least Median Squares (LMS). These median-based methods offer a more robust approach to partitioning data in causal tree algorithms by reducing sensitivity to extreme values and affecting bias and precision in treatment effect estimation. Through a simulation study, we assess the precision, bias, and confidence interval coverage of our proposed methods relative to existing causal tree algorithms. We further use median-based splitting rules within two empirical applications. First, we estimate the electoral effects of a Mexican conditional cash transfer program on precinct-level observations. Second, we quantify effect heterogeneity of antiretroviral treatments on HIV-positive adults.