Estimation And Applications Of Partially Varying Coefficient Single-index Spatial Regression Models

Partially varying coefficient single-index regression model combines the characteristics of the varying coefficient regression model and the single-index regression model.It can not only overcome "the curse of dimensionality" in non-parametric regression model,but also be used to study the nonlinearity between the variables.Its estimation method has been widely applied in economics,management and other disciplines.Because many response variables have spatial correlation in real economic problems,it is necessary to extend the partially varying coefficient single-index regression model to the partially varying coefficient single-index spatial regression model,the aim is to describe the relationship between explaining variables and response variables more accurately.We find that the theory,method and application of the model are still in blank.Therefore,it is of great theoretical significance and application value to study the model in depth and systematically.On the basis of sorting out the existing research literature,this paper has completed the following research contents:(1)Proposed two new Models,including the partially varying coefficient single-index spatial lag regression model and the partially varying coefficient single-index spatial error lag regression model;according to the characteristics of the new model,the profile quasi-maximum likelihood estimation method of the two models was constructed,and the estimation of parameters and the unknown function of non-parameters was given respectively;(2)According to the characteristics of the new model,the profile quasi-maximum likelihood estimation method of the two models is constructed,and the estimation of the unknown function of parameters and non-parameters is given respectively;(3)Monte Carlo simulation was used to investigate the performance of the estimated under small sample;(4)The estimation methods of the two models are respectively used to study the influencing factors of Boston House Price and the socio-economic factors of PM2.5 in China.The results of Monte Carlo numerical simulation showed that:(1)With the increase of sample size,the sample standard deviation Std.dev and root-mean-square error RMSE of the parameter estimation of the two models both decreased rapidly,indicating that the parameter estimation effect has good preformance;(2)The mean absolute error of the unknown function estimation of the two models also decreases rapidly,indicating that the unknown function estimation has good performance under small sample;(3)Byintroducing Case and Rook weight matrices with different complexity,the simulation results show that the estimation effect of spatial correlation coefficient is affected by spatial complexity to some extent.The more complex the spatial structure is,the greater the estimation error will be,while the smaller the impact on other estimation will be.In general,the estimation methods of the model have good performance under small sample and can be applied to study the actual data research.This paper made from two aspects of the application research:(1)The estimation method of the partially varying coefficient single-index spatial lag regression model was applied to analyze the influence factors of Boston House Prices,the results show that the low education hath ratio have negative impact on Boston House Prices with the change of crime rate per capita.The proportion of teachers and students in towns has positive impact on House Prices with the change of crime rate per capita.The proportion of blacks in towns less with the change of per capita crime rate.The linear combination of the proportion of urban non-retail land and the weighted distance to the five urban districts of Boston has negative impact on House Prices.(2)The estimation method of the partially varying coefficient single-index spatial error lag regression model was applied to analyze the socio-economic factors of PM2.5 in China,the results show that the power consumption,urban green coverage rate and industrial dust emission change with per capita GDP,and the linear combination of population density and the proportion of the secondary industry have positive impact on PM2.5 concentration,while the number of buses has negative impact on PM2.5 concentration with the change of per capita GDP.