  The Distributional Random Forest (DRF) is a recently introduced Random Forest
algorithm to estimate multivariate conditional distributions. Due to its
general estimation procedure, it can be employed to estimate a wide range of
targets such as conditional average treatment effects, conditional quantiles,
and conditional correlations. However, only results about the consistency and
convergence rate of the DRF prediction are available so far. We characterize
the asymptotic distribution of DRF and develop a bootstrap approximation of it.
This allows us to derive inferential tools for quantifying standard errors and
the construction of confidence regions that have asymptotic coverage
guarantees. In simulation studies, we empirically validate the developed theory
for inference of low-dimensional targets and for testing distributional
differences between two populations.
