Research On Geographically Weighted Regression Model For Panel Dat

Panel data has the two-dimensional nature of observation time and observation individual,and has irreplaceable advantages in describing the dynamic change law of things.The panel data models constructed on this basis,including static panel data model,dynamic panel data model and spatial panel data model,has played an important role in the application research of many fields.However,most of the existing panel data models assume that the relationship between independent variables and dependent variables is linear,which fails to reflect the complex relationship between independent variables and dependent variables,resulting in a large deviation between the inference results and the actual situation,or even contrary.In order to overcome the limitation of linear relationship,based on semi parametric and nonparametric modeling methods,this paper proposes two kinds of new panel data models,and studies statistical inference and empirical problems.The first part of the paper studies the setting and parameter estimation of the geographically weighted regression model of panel data.Based on the static panel data model,the model uses the semi parametric modeling method,integrates the idea of spatial variable coefficient,introduces the unknown function about geographical location into the coefficients of the model,and fully considers the geographical location factor in the establishment of the model.It is a new expansion form of panel data model in spatial dimension,which is different from the traditional spatial panel data model.For the new model,the paper proposed within local least square method and profile least square method to estimate the unknown coefficient function in the model,and further considered the hypothesis test of the model.The second part of the paper studies the setting and parameter estimation of the geographically weighted regression model of dynamic panel data.The model is based on the nonparametric modeling method,and also introduces the unknown function about the geographical location.Based on the geographically weighted regression estimation method,combined with the instrumental variable method,the estimation of the unknown coefficient function is derived,and the hypothesis test is carried out.The third part of the paper uses the panel data of relevant indicators of 29 provinces in China from 2001 to 2012,and the longitude and latitude information of 29 provincial capitals to study the spatial distribution characteristics and socio-economic influencing factors of PM2.5.The two models proposed in this paper are compared with the linear least squares regression model,which proves that the new model has advantages in the study of practical problems.Using semi parametric and nonparametric modeling methods,this paper puts forward two kinds of new panel data models,which enriches the model form of panel data and the content of spatial econometrics.It is an expansion of panel data model in spatial dimension and provides a new statistical method for the research of practical problems.