标题： 概率回归树中缺失数据的处理：方法及在R中的实现 显示英文标题

标题： Handling Missing Data in Probabilistic Regression Trees: Methods and Implementation in R

摘要： 概率回归树（PRTrees）通过引入将每个数据点与树的不同区域相关联的概率函数，扩展了传统决策树，提供了平滑的决策和连续响应。 本文介绍了一种能够通过三种不同方法处理协变量中缺失值的PRTrees适应方法：（i）均匀概率方法，（ii）部分观测方法，（iii）降维平滑技术。 所提出的方法保持了PRTrees的可解释性特性，同时将其适用性扩展到不完整数据集。 在MCAR条件下进行的模拟研究展示了每种方法的相对性能，包括与传统回归树在平滑函数估计任务中的比较。 所提出的方法以及原始版本已在R中开发，具有高度优化的例程，并在PRTree包中分发，可在CRAN上公开获得。 在本文中，我们还介绍了并讨论了PRTree包的主要功能，为研究人员和实践者提供了新的工具用于不完整数据分析。 显示英文摘要

摘要： Probabilistic Regression Trees (PRTrees) generalize traditional decision trees by incorporating probability functions that associate each data point with different regions of the tree, providing smooth decisions and continuous responses. This paper introduces an adaptation of PRTrees capable of handling missing values in covariates through three distinct approaches: (i) a uniform probability method, (ii) a partial observation approach, and (iii) a dimension-reduced smoothing technique. The proposed methods preserve the interpretability properties of PRTrees while extending their applicability to incomplete datasets. Simulation studies under MCAR conditions demonstrate the relative performance of each approach, including comparisons with traditional regression trees on smooth function estimation tasks. The proposed methods, together with the original version, have been developed in R with highly optimized routines and are distributed in the PRTree package, publicly available on CRAN. In this paper we also present and discuss the main functionalities of the PRTree package, providing researchers and practitioners with new tools for incomplete data analysis.