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）是近期提出的一种用于估计多元条件分布的随机森林算法。由于其通用的估计流程，该方法可被应用于广泛的目标估计，例如条件平均处理效应、条件分位数和条件相关性。然而目前关于DRF的研究仅能提供其预测的一致性与收敛速率结果。我们刻画了DRF的渐近分布特征，并开发了相应的自助法近似方法。这使得我们能够推导出用于量化标准误的推断工具，并构建具有渐近覆盖保证的置信区域。在模拟研究中，我们通过低维目标推断与双总体分布差异检验两个场景，对理论推导结果进行了实证验证。