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.

翻译：分布随机森林（DRF）是一种近期提出的随机森林算法，用于估计多元条件分布。由于其通用估计流程，该方法可应用于估计多种目标变量，如条件平均处理效应、条件分位数和条件相关性。然而，目前仅有关于DRF预测一致性和收敛速率的研究结果。本文刻画了DRF的渐近分布，并开发了其自助法近似。据此，我们推导出用于量化标准误差的推断工具，并构建了具有渐近覆盖保证的置信域。通过仿真研究，我们实证验证了所提理论在低维目标推断及两总体分布差异检验中的有效性。