Parameter Estimation And Application Of Spatial Varying Coefficient Quantile Regression Models

Analysis and statistical modeling of spatial structure data has always been a hot topic in many scientific fields.The simple global regression modeling not only ignores the data information of spatial geographic location,but also fails to meet the needs of research when the covariables have spatial non-stationary effects.Spatial Varying Coefficient Models(SVCMs)is an effective tool to study spatial nonstationary data.It can be used to study the relationship between spatial dependence and spatial nonstationary properties.In recent years,the research on SVCMs in the meaning of mean value is common.However,due to the complexity of data generation mechanism,the mandatory assumption of Gaussian error in mean regression method is difficult to satisfy in real life.The quantile regression estimation method can overcome this defect.Therefore,it is necessary to generalize mean regression to quantile regression estimation.At First,this thesis introduces the spatial varying coefficient nonparametric regression model,and develops a quantile regression estimation method based on bivariate penalty spline approximation.This estimation method can not only deal with the spatial region with complex boundary and irregular shape,but also shows the interpretation ability under different quantile levels.In two different cases,the theoretical properties of the proposed estimator,the rate of convergence and asymptotic distribution,are given respectively.For the estimation process of parameters,an iterative algorithm based on Alternating Direction Multiplier Method(ADMM)is proposed to solve the model.To test the goodness-of-fit of the model,a goodness-of-fit test method based on Boostrap method is proposed in this thesis,and the test implementation algorithm is given.Based on the good performance of composite quantile regression,the thesis also presents the composite quantile regression estimator of bivariate penalty spline approximation of the model and its implementation algorithm.The numerical simulation results show that the proposed estimation method is more robust than the mean value.Secondly,considering the coexistence of stationary effect and non-stationary effect of spatial data,the Spatial Partial Linear Varying Coefficient Models(SPLVCMs)is proposed.This model is a semi-parametric model,including linear part and non-parametric part,which represent the stationarity and non-stationarity effect of spatial covariables respectively.For the parameter estimation,a non-parametric approximation quantile regression estimation method based on bivariate penalty splines is proposed,and the theoretical properties of the linear part and the non-parametric part estimator are studied.A parameter estimation algorithm based on ADMM is proposed to realize the model.In the numerical simulation stage,the simulation results under different conditions show that the proposed method has obvious advantages under non-normal error,and the estimation results are more robust and effective.Finally,this thesis uses actual data of Florida unemployment rate and air quality data of China to verify the application value of the proposed method.The results show that the proposed models can fully describe the nonstationary influence relationship between covariates and response variables,which can provide a new method and theory for subsequent application research.