We propose a theoretical study of two realistic estimators of conditional distribution functions and conditional quantiles using random forests. The estimation process uses the bootstrap samples generated from the original dataset when constructing the forest. Bootstrap samples are reused to define the first estimator, while the second requires only the original sample, once the forest has been built. We prove that both proposed estimators of the conditional distribution functions are consistent uniformly a.s. To the best of our knowledge, it is the first proof of consistency including the bootstrap part. We also illustrate the estimation procedures on a numerical example.
翻译:我们提议对使用随机森林的有条件分配功能和有条件的量化的两种现实估计器进行理论研究。估计过程在建造森林时使用原始数据集生成的靴套样本。对诱套样本进行再利用,以确定第一个估算器,而第二个样本只要求原始样本,一旦森林建成,则仅要求原始样本。我们证明,提议的有条件分配功能的估算器一致。据我们所知,这是包括靴套部分在内的一致性的第一个证据。我们还用数字示例来说明估算程序。