Random Forest Estimation Of Partially Linear Varying-coefficient Model

Partial linear varying-coefficient(PLVC)model has both the interpretability of linear model and the strong expressive ability of varying-coefficient model.It has been paid more attention in the fields of statistics,economics and medicine.The key problem in model research is parameter estimation and statistical inference,but the existing estimation methods are not effective when the dimension of nonparametric variables is high.In this paper,we mainly use random forest to study the estimation problem of PLVC model.We use random forest as a weighted adaptive nearest neighbor method to estimate the nonparametric part of the model,and then the parameter part can be estimated.Because random forest is suitable for high-dimensional data,as an ensemble method,it is robust in the face of noise data and can identify the heterogeneity between data.Therefore,the random forest estimation of PLVC model proposed in this paper can be applied to the case of nonparametric partial variables with high dimension,noise variables and heterogeneity.These properties are discussed and verified again in the simulation part of Chapter 3.In the Chapter 2,the estimation algorithm is described in detail and the estimator is analyzed theoretically.In the estimation algorithm,honest tree is used as the base predictor of random forest,which makes the estimation method insensitive to the tuning of hyperparameter.In the theoretical analysis part,the asymptotic normality of parameter estimator is proved under certain conditions.In the empirical part of Chapter 3,the estimation method is applied to the air quality data of Shandong Province,and the PM2.5 concentration regression model is established to predict.The change of coefficients also provide a certain reference for pollution prevention and control.