Code and synthetic data for "Wilcoxon Random Forests for Robust Distributional Prediction"

We propose a Wilcoxon random forest (WRF) for prediction of outcome distributions. The method grows trees using a rank-based splitting criterion that targets stochastic separation between the outcome distributions in child nodes and estimates conditional distributions using forest-weighted empirical CDFs. The WRF can be used to estimate conditional quantiles, means, and threshold probabilities. Because the splitting criterion depends only on outcome ranks, WRF is invariant to strictly increasing transformations and can accommodate continuous, ordinal, and mixed outcomes, including biomarkers with detection limits. We establish consistency, we investigate performance with simulations, and we illustrate the method by predicting HIV outcomes in a multicenter Latin American cohort.