Research And Application Of Estimation Method And Variable Selection Method Of The Additive Spatial Autoregressive Model

In the field of spatial econometrics,the spatial autoregressive model has a very important position.The model has been known by a lot of people and has been applied to all walks of life since the model was put forward.In this time,the growth of space data is explosive.This model has a very broad application prospects.The relationship between each regressor and dependent variable is linear relationship in traditional spatial autoregressive model.It makes the application range of the model has some limitations,obviously,when the relationship between some regressors and dependent variable is unknown or nonlinear,the model is not applicable.If we take these nonlinear regressors as linear parts of the model,estimation error of dependent variable is likely to be increased.This is one of disadvantages of the traditional spatial autoregressive model.In order to make up for this disadvantage,this paper proposes the spatial additive autoregressive model and proposes the estimation method about the model,creatively.Then the estimation method is extended to estimation of the additive partially linear spatial autoregressive model.Monte Carlo Simulation study shows that when using the proposed estimation method to estimate the predefined additive spatial autoregressive model,the parametric part of the model is able to achieve good effect of estimation,estimation of parameters have certain accuracy;the Nonparametric part of the model is able to achieve good fitting result,showing functional relationship between each regressor and dependent variable.In addition,this paper proposes variable selection method about the additive spatial autoregressive model,creatively.Then the variable selection method is extended to variable selection of the additive partially linear spatial autoregressive model.Variable selection method can not only play the role of variable selection,but also play the role of model selection,identify the specific influence each variable on the dependent variable(including: linear effect,nonlinear effect,no effect).Monte Carlo Simulation study shows that it is obvious that the role of the variable selection method on variable screening.The variable selection method can more accurately identify the specific types of effect from regressors on dependent variable.Finally,the estimation method and the variable selection method of the additive partially linear spatial autoregressive model,which are based on the estimationmethod and the variable selection method of the additive spatial autoregressive model,are both used in the data set about Boston housing prices.First,this paper builds the model and carries on the model prediction.In this model,the variable,which denotes median of house prices,is dependent variable.The rest of the variables are independent variables except the latitude and the longitude.Then,this paper uses the variable selection method on the model to implement model selection,identify the specific types of effect from regressors on dependent variable.