  We propose a method for constructing a confidence region for the solution to
a conditional moment equation. The method is built around a class of algorithms
for nonparametric regression based on subsampled kernels. This class includes
random forest regression. We bound the error in the confidence region's nominal
coverage probability, under the restriction that the conditional moment
equation of interest satisfies a local orthogonality condition. The method is
applicable to the construction of confidence regions for conditional average
treatment effects in randomized experiments, among many other similar problems
encountered in applied economics and causal inference. As a by-product, we
obtain several new order-explicit results on the concentration and normal
approximation of high-dimensional $U$-statistics.
