Research On Two Kinds Of Semiparametric Spatial Panel Data Model

In recent years, spatial panel data model has been got attention by statisticians and econometricians, in-depth research in theory, and is widely applied to various types of practical problems analysis. However, most of existing research assumes that the relationship between the dependent variable and independent variables are the parameter form, especially linear form. As we all know, on one hand, model in the error form will cause inference results deviate from the actual situation. On the other hand, in order to better explore the complex relationship between dependent variable and independence variable and improve model flexibility, some non-parametric and semi-parametric modeling methods has been proposed in the past two decades, and applied to all kinds of complex data analysis. Naturally, using semi-parametric models to analyze spatial panel data has been got the attention, and many types of semi-parametric spatial panel data models have been proposed and studied recently. This paper presents two new types of semi-parametric spatial panel data model, and proposes the corresponding estimation and testing methods.The first part presents a class of partially linear spatial autoregressive panel data model with fixed effects, gives the parametric component and nonparametric component estimation in the model using profile likelihood method based on local linear smoothing technology, construct a test statistic for spatial effect utilizing profile generalized likelihood ratio method, obtain the test p-value utilizing bootstrap method, and finally verify the effectiveness of the proposed method using numerical simulation.The second part proposes a class of varying coefficient spatial autoregressive panel data model with fixed effects, similarly gives the unknown component estimations based on the likelihood method, test the spatial effect utilizing profile generalized likelihood method. In addition, we have studied a class of generalized model, namely, estimation of partially varying coefficient spatial autoregressive panel data model with fixed effects. Numerical simulation shows that the proposed method is effective and feasible.This paper proposed two new types of spatial econometric models by means of semi-parametric modeling. The results enrich the research contents of semi-parametric model and spatial econometric, and provide a more flexible method of statistical modeling for the analysis of spatial panel data.