Variable Selection And Application Of Semiparametric Spatial Autoregressive Model Based On Orthogonal Projection

In the parametric-space autoregressive model,the relationship between response variables and covariates may sometimes be nonlinear,and even the specific form of the nonlinear relationship is unknown.Under the condition of variables containing complex correlation,it is not appropriate to use the parametric space autoregressive model for statistical analysis,while the semi-parametric space autoregressive model can well solve the endogenous problem of the model and then improve the validity and consistency of the estimation.At the same time,the variable selection theory is an important research topic of the semiparametric space autoregressive model,because ignoring any important covariates will lead to serious deviations in the results,and at the same time,including many false covariates will significantly reduce the effectiveness of the model estimation.Therefore,this thesis proposes a variable selection method based on orthogonal projection by establishing a partial linear space autoregressive model and a partial linear additive space autoregressive model,combining the QR decomposition technique of a matrix and the method of penalty generalized moment estimation,and proves that the estimation of parametric and nonparametric components is consistent.It also gives the asymptotic distribution of parametric components and the optimal nonparametric convergence rate.Finally,the proposed method has proven to be robust and effective.Compared with many variable selection methods,the method proposed in this thesis can select important covariates in parameter components independently,without any influence from non-parametric components,and can also identify the significance of spatial effects.Secondly,the research on the selection mechanism of effective instrumental variables has a lower computational burden,and the research process is relatively simple,which can improve the effectiveness of the estimation and be easily implemented in practice.In recent years,China’s online shopping industry has been one of the key factors affecting economic development.Therefore,using the variable selection method of the partial linear spatial autoregressive model proposed in this thesis to analyze online shopping data with spatial effects and find important indicators affecting online shopping factors has certain policy significance.The results of empirical analysis show that the per capita disposable income of residents and regional GDP have the most significant impact on residents’ online shopping consumption level;secondly,the Alipay account registration index and retail sales of social goods indirectly affect the development of the online shopping industry,and the impact is positive;at the same time,the proportion of urban population,education level,and the number of logistics outlets affect the consumption level of residents online shopping to a certain extent.Finally,through the nonparametric estimation fitting results,we can see that the level of online shopping consumption will increase with the increase in the proportion of the tertiary industry,so adding more online shopping platforms appropriately will effectively stimulate the consumption potential of residents.