Uniform Inference for Generalized Random Forests

Random forests are a powerful tool in nonparametric data science and have been studied intensively for their theoretical properties and applicability in many scientific fields. Among the newest insights into their asymptotics are extensions towards Generalized Random Forests, with a central limit theorem allowing for the study of the point-wise influence of features/variables identified as the solution to various forms of local moment equations. Here, we extend these findings in Athey et.al (2019) towards uniformity, hence allowing us to check whether over a range of feature values one observes significant effects. Such an extension is a welcome practical tool since it allows more powerful statements independent of fixed feature values. A feasible multiplier bootstrap procedure is developed to determine the critical values for the uniform confidence bands. Numerical simulations justify that this 'wild bootstrap'-type method gives reliable coverage for inference, even in small samples. As real data applications, we revisit the mother's labor force participation analysis %based on the sample used in Athey et.al (2019) from the 1980 U.S. Census and find that the father's income doesn't always drive the causal effect of having a third child on women's labor force participation. Additionally, we extend the emergency department utilization study Denteh et. al (2022) based on the Oregon Health Insurance Experiment to demonstrate how uniform confidence bands offer further insights into Medicaid's treatment effects, revealing multifaceted relationships between age, gender, and prior benefit levels.