Spatial Lag Quantile Regression Model Bases On Lasso With Time Varying Coefficients And Its Application

Traditional regression analysis mainly uses the mean regression model,and the mean regression model estimates the conditional expectation of the dependent variable and cannot describe the distribution of the variable.The result reflects the position information of the conditional distribution of the dependent variable,and cannot describe the scale or shape of the distribution.The application conditions of the quantile regression model are more relaxed than the traditional mean regression model,which can make up for the above shortcomings of the mean regression model.Due to the various advantages of quantile regression models,after more than forty years of development,scholars have applied quantile regression to various fields.The quantile regression model is combined with the spatial measurement model to form a spatial quantile model;the quantile regression model is combined with the variable coefficient model to form a variable coefficient quantile model.In addition,variable selection has been a hot research direction in statistics since it was proposed in the 1960s.This paper combines the quantile regression model with the spatial measurement model,the variable coefficient model to construct a time-varying coefficient spatial lag quantile regression model;On this basis,this paper adds a penalty function to the parameter estimation process of the model to make the estimation result more accurate.The effectiveness of the "three-step estimation method" proposed in this paper is discussed through numerical simulation.The study found that this method has the advantages of high accuracy and strong stability under different variances and different sample sizes.After that,combined with the variable selection method,we discussed the sparseness of different coefficients,the correlation degree of different variables,whether there is strict group correlation,different disturbance items,and different sample sizes.In the empirical part,this article explores the influencing factors of environmental quality and constructs a time-varying coefficient spatial lag quantile regression model based on Adaptive Lasso.The degree of influence of quality is relatively large,and the degree of influence of different variables on environmental quality can also be seen over time.