Statistical Inference And Applications Of Geographically Weighted Regression Models

Spatial data refers to all types of data objects or elements that exist in geospatial or horizon.Different from time series and cross-section data,spatial data contains not only sample attribute information,but also geographic location information.Spatial data exist in many research fields,such as econometrics,geography and environmental science.With the advent of the era of big data,all walks of life need to use data to drive business.Relevant industries have higher and higher requirements for the application of spatial data,and the research and application of theoretical methods of spatial data have attracted more and more attention.Spatial heterogeneity and spatial correlation,as the two most common important attributes of spatial data,have been widely concerned by researchers in recent years.In terms of analyzing spatial heterogeneity,geographically weighted regression model(GWR)is the most widely used analysis tool.The model assumes that the regression coefficient changes with spatial location,so the spatial heterogeneity of regression relationship can be reflected by estimating the spatial change mode of coefficients.Based on the GWR model,Fotheringham et al.Proposed the semi parametric form of the model-mixed GWR models.Recently,these two models have been widely popularized in theory and practical application,but there are still some deficiencies in the existing theoretical and practical application research.For example,the related research of mixed GWR models ignores the possible Heteroscedasticity in the model;Although the model can better reflect spatial heterogeneity,but ignore spatial correlation.Most of the practical application cases based on geographically weighted regression use the classical GWR Model Based on a single bandwidth,ignoring the impact of the spatial heterogeneity of each coefficient function on the estimation of the coefficient function.Therefore,in order to make up for these shortcomings,this paper discusses the above problems.The main research contents include the novel profile likelihood estimation of the mixed GWR models,the spatial heteroscedasticity test of the mixed GWR models,and the orthogonal projection estimation of the mixed GWR model in the presence of heteroscedasticity,Generalized method fo moments estimations for mixed GWR models with erro spatial autocorrelation,Application of multi-scale GWR,etc.The main research contents are as follows:The first chapter focuses on the research status,research significance and existing problems of GWR models and mixed GWR models.In addition,it roughly states the research content,research framework and research innovation of this paper.Chapter 2,a novel profile least squares estimation method for mixed GWR model is given.based on the idea of local linear fitting of nonparametric models,a new contour least squares estimation method for mixed GWR model is proposed,and the asymptotic properties of the estimator are given.Through Monte Carlo data simulation,the accuracy of the method proposed in this chapter for the estimation of model constant coefficients and coefficient functions is investigated,and compared with the two-step estimation method.Finally,an empirical case shows the effectiveness and practical application of the proposed method.In the third chapter discusses the test of spatial heteroscedasticity of mixed GWR models.Under the framework of mixed geographically weighted regression model,the sample data come from different spatial and geographical locations,so it often violates the homoskedasticity assumption of the model about the error term.The heteroscedasticity of the model error term may have an adverse impact on the coefficient estimation of the mixed GWR model,which seriously affects the reliability of subsequent statistical inference.Based on the new contour least squares estimation method of the mixed GWR model,this chapter proposes two test statistics for the spatial heteroscedasticity of the mixed geographically weighted regression models for the first time.One is a test statistic constructed based on the sum of squares of residuals,and the other is a test statistic constructed based on the square root of the absolute value of residuals,For the first test statistic,the p value of the test is calculated by the third-order moment chi square approximation method.The ability and test efficacy of the two test statistics to control the first kind of error are evaluated by Monte Carlo data simulation.Finally,an actual data analysis is given to demonstrate the effectiveness of the proposed test method.In the fourth chapter mainly studies the estimation of mixed GWR model in the presence of heteroscedasticity,and proposes a new orthogonal projection estimation method for mixed GWR model with heteroscedasticity.In the estimation process,the ideas of orthogonal projection of matrix,local linear estimation of nonparametric regression,kernel estimation and weighted least squares estimation are combined.The estimated values of constant coefficient,coefficient function and variance function in the model are given in three steps,and the specific expression of estimator is given.Furthermore,the consistency and asymptotic normality of the estimators are given.The effectiveness of the proposed method is verified by data simulation,The proposed estimation method is applied to the practical application of the actual data demonstration method.In the fifth chapter mainly studies the parameter estimation and statistical inference of error autocorrelation mixed GWR models.For the data with both spatial heterogeneity and spatial correlation,this chapter proposes an error autocorrelation mixed GWR models.As an effective fusion of mixed GWR model and spatial error model,the model can effectively deal with spatial correlation through the spatial correlation structure contained in the error term,while maintaining the characteristics that the mixed GWR model can reflect the global and spatial heterogeneity of regression relationship at the same time,Therefore,it can fully tap the potential information contained in spatial data itself.In this chapter,the generalized method of moments and local linear estimation method are combined to estimate the model parameters,and the asymptotic normality of the estimator is proved under certain regular conditions.The finite sample performance of the estimation method is discussed through Monte Carlo data simulation.Finally,an actual case is given to illustrate the application of the proposed model and method.In the sixth chapter makes an empirical study on the spatial heterogeneity of carbon emissions and its influencing factors of 284 prefecture level cities in China in 2005 and 2012 by using multi-scale GWR model,The empirical results not only study the spatial heterogeneity of carbon emissions and its influencing factors,but also further explore the action scale of each explanatory variable.