Simultaneous Inference for Local Structural Parameters with Random Forests

Abstract: We construct simultaneous confidence intervals for solutions to conditional moment equations. The intervals are built around a class of nonparametric regression algorithms based on subsampled kernels. This class encompasses various forms of subsampled random forest regression, including Generalized Random Forests (Athey et al., 2019). Although simultaneous validity is often desirable in practice -- for example, for fine-grained characterization of treatment effect heterogeneity -- only confidence intervals that confer pointwise guarantees were previously available. Our work closes this gap. As a by-product, we obtain several new order-explicit results on the concentration and normal approximation of high-dimensional U-statistics.