Estimation And Applications Of A Class Of Spatially Varying Coefficient Models

Spatial statistics is a research field devoted to the statistical analysis of spatial data.A common problem in spatial data analysis is to identify the relationships that exist between variables,and spatial regression model is the main research tool,which can be divided into global spatial regression model and local spatial regression model.The global spatial regression model takes the spatial correlation research as the leading role,and mainly explores the spatial interaction effect between different variables and error terms.Local regression model focuses on spatial heterogeneity,and all samples exhibit different statistical characteristics of interest.This paper focuses on spatial heterogeneity and studies a class of spatially varying coefficient models(SVCM)whose regression coefficient is a binary function of spatial position.The main content is as follows:Firstly,a new adaptive estimation approach is proposed for the spatially varying coefficient models with unknown error distribution,unlike geographically weighted regression(GWR)and local linear geographically weighted regression(LL),this method can adapt to different error distributions.A generalized Modal EM(GMEM)algorithm is presented to implement the estimation,and the asymptotic property of the estimator is established.Simulation and real data results show that the gain of the new adaptive method over the GWR and LL estimation is considerable for the error of non-Gaussian distributions.Secondly,the tensor product spline estimation of the function coefficient in the spatially autoregression varying coefficient model is given,and the convergence rate of the estimator is established when the error is independent.The performance of the estimators is evaluated through simulations,which show that the method is more efficient than the calculation of geographically weighted regression(GWR),and the application of the method is illustrated through an environmental data example.Thirdly,a spatially varying coefficient models with weighted mean distance is devoloped,and analyzes the spatial pattern and influencing factors of digital economy enterprise density in Guangdong Province based on the panel data of city in Guangdong Province from 2016 to 2020.It is found that the density of regional digital economy enterprises in Guangdong province is significantly different,and the regional pattern presents a decreasing trend of "One Core Region,One Belt and One Area",and the regional differences are decreasing year by year;The density of digital economy enterprises in Guangdong province is significantly spatial positive correlated,and the location factor is one of the important factors affecting the density of digital economy enterprises;Among the influencing factors,the impact of material capital investment density on the density of digital economy enterprises in various regions is positive and strong.At last,a prediction model for net anthropogenic nitrogen inputs(NANI)is built based on the recent 30 years of NANI data from the watershed of the Yangtze River in China,with readily available and complete socio-economic predictor variables(per gross domestic produt,population density)through a hierarchical spatially varying coefficient process(HSVC)model,which exploits underlying spatial associations within 11 sub-basins and the spatially-varying impacts of predictor variables to improve the accuracy of NANI prediction.This hierarchical spatially varying coefficient model performs better compared to the Guassian process model and the spatio-temporal dynamic linear model.The point prediction and 95%interval prediction of NANI in the watershed of the Yangtze River for 2025 and 2030 were also provided.Our approach provides a simple and easy-to-use method for NANI prediction.