Expectile regression forest: A new nonparametric expectile regression model
Chao Cai, Haotian Dong, Xinyi Wang
Abstract
Abstract Classical nonlinear expectile regression has two shortcomings. It is difficult to choose a nonlinear function, and it does not consider the interaction effects among explanatory variables. Therefore, we combine the random forest model with the expectile regression method to propose a new nonparametric expectile regression model: expectile regression forest (ERF). The major novelty of the ERF model is using the bagging method to build multiple decision trees, calculating the conditional expectile of each leaf node in each decision tree, and deriving final results through aggregating these decision tree results via simple average approach. At the same time, in order to compensate for the black box problem in the model interpretation of the ERF model, the measurement of the importance of explanatory variable and the partial dependence is defined to evaluate the magnitude and direction of the influence of each explanatory variable on the response variable. The advantage of ERF model is illustrated by Monte Carlo simulation studies. The numerical simulation results show that the estimation and prediction ability of the ERF model is significantly better than alternative approaches. We also apply the ERF model to analyse the real data. From the nonparametric expectile regression analysis of these data sets, we have several conclusions that are consistent with the results of numerical simulation.