众数回归森林模型及其在收入分配研究中的应用

Modal Regression Forest Model and Its Application in Income Distribution Research

为解决传统非参数众数回归模型没有考虑解释变量间复杂交互影响的局限,文章将众数回归与机器学习方法相结合,提出了一个新的非参数众数回归模型:众数回归森林模型。该模型一方面充分考虑了各个解释变量之间的交互影响;另一方面采用Bagging技术汇总多个众数回归树的结果,提高了预测性能。数值模拟结果表明:第一,与线性众数回归模型和众数回归树模型相比,众数回归森林模型极大地提高了估计和预测精度;第二,当数据为偏态分布时,众数回归森林模型的估计和预测精度显著优于中位数回归森林和均值回归森林模型。此外,将众数回归森林模型应用于收入分配研究中,得到了与中位数回归森林和均值回归森林模型不同的结果。

In order to solve the limitation that the traditional non-parametric modal regression model does not consider the complex interaction between explanatory variables,this paper combines modal regression with machine learning method to propose a new non-parametric modal regression model:Modal Regression Forest(MRF).On the one hand,this model fully considers the interaction among explanatory variables.On the other hand,Bagging technique is used to summarize multiple mode regression tree models to improve the prediction performance.The results of numerical simulation are as follows:Firstly,compared with the linear modal regression model and the modal regression tree model,the modal regression forest model greatly improves the estimation and prediction accuracy.Second,when the data are skewed,the estimation and prediction accuracy of the modal regression forest model is significantly better than that of the median regression forest model and the mean regression forest model.In addition,the modal regression forest model is applied to study the income distribution,and the results are different from the median regression forest model and mean regression forest model.