Variable Selection Of Partially Linear Spatial Autoregressive Models

With the advent of the era of big data,the amount of data obtained has increased dramatically.These data bring a lot of information and increase the complexity of the model.Therefore,how to use existing data,eliminate irrelevant variables,and select significant variables from complex variable information to construct statistical models has become one of the hot issues in recent years.At present,many literatures have conducted theoretical research on semi-parametric or nonparametric spatial autoregressive models,but there are few theoretical studies in the case of outliers or non-normal distribution of errors.This thesis mainly studies the partially linear spatial autoregressive model.Firstly,the non-parametric part is fitted by B-spline technique.Then,two novel variable selection processes based on orthogonal projection technique are proposed,they are named as variable selection process based on exponential square loss and variable selection process based on Expectile regression.These two variable selection processes can simultaneously perform model selection and parameter estimation,and identify the significance of spatial effects,they also can select important covariates in the parameter components without affecting the nonparametric components.The variable selection process based on exponential square loss can handle data with outliers,it is more robust than the variable selection process based on least squares.The variable selection process based on Expectile regression uses the entire distribution information of the variable,and the estimation is more effective for thick tail and the skewed data.At the same time,the consistency,sparsity and asymptotic normality of these two methods are proved under some regular conditions.In addition,we verify the performance of these two methods by numerical simulation,and the variable selection process based on exponential square loss is further applied to a real data analysis.