Estimation And Application Of Semiparametric Spatial Varying-Coefficient Autoregressive Model

Spatial data is widely existed in economics,geography,environment,management and other fields.The correlation and non-stationarity of spatial data are the core content of spatial statistics.The classical spatial autoregressive model with spatial lag terms and the spatially variable coefficient model are respectively designed for spatial correlation and spatial non-stationarity,failing to incorporate both into the same regression model and makes it impossible to effectively design model to data sets that are both correlation and non-stationary.Therefore,the model that can simultaneously analyze the spatial data correlation and non-stationarity under the semiparametric regression framework is a hot topic in current spatial statistics.In this paper,the function with spatial position is introduced as regression coefficient into the spatial autoregressive model to construct a semiparametric spatial varying-coefficient autoregressive model,which allows the influence of some independent variables on the dependent variable changes with the geographical position,and reflects the space correlation.Firstly,the paper studies the estimation method of semiparametric spatial varying-coefficient autoregressive model,and then explores whether the model regression relationship has spatial non-stationarity through hypothesis testing.Finally,the model estimation method and hypothesis testing method are applied to the population urbanization data of China.The main contents are as follows:1.For the estimation of the lag term coefficient,the constant value coefficient and the variable coefficient part of the model,constructing the instrumental variables,using the two-stage least squares method to estimate the lag term coefficient and the constant value coefficient of the semiparametric spatial varying-coefficient autoregressive model.Using the local linear geographic weighting method to estimate the spatial variable coefficient parts.Designing the simulation experiment,the accuracy of the semiparametric spatial varying-coefficient autoregressive model estimation method is verified by the mean deviation and standard error indicators.2.For the hypothesis testing problem of spatial non-stationarity of the semiparametric spatial varying-coefficient autoregressive model,constructing the generalized likelihood ratio statistic based on residual,the bootstrap method is used to obtain the p-value of the hypothesis testing.The simulation experiment is designed to confirm the bootstrap test method based on residual has strong efficacy.3.Using the population urbanization data of 31 provinces in China in 2015,based on the semiparametric spatial varying-coefficient autoregressive model,analyzing the effects of macro factors such as tertiary industry,secondary industry,urban-rural income gap and foreign investment on the population urbanization.The results show that there is spatial correlation between population urbanization,the development of the secondary and tertiary industries in the western,central and eastern regions has showed a strong spatial non-stationary impact on the urbanization of the population.