Statistical Inference Of Spatial Quantile Durbin Model

Spatial regression model is a common modeling method of spatial data.Spatial data generally show spatial dependence.So adding lag effect with dependent variables in traditional spatial regression model can solve this problem very well.Moreover,in the process of spatial data modeling,the change of independent variable of one observation value can potentially affect the dependent variable of other observation values,so adding lag effect of independent variable in the model can more truly reflect the data relationship.Heterogeneity is also a major feature of spatial data,so when there is heteroscedasticity in data,quantile regression can describe spatial process more accurately.Quantile estimation method does not need the assumption that the error term satisfies the normality,thus relaxing the conditions for the establishment of the model and making it more applicable.Furthermore,the Bayes method also has an important application in the spatial quantile regression model.We study the spatial Durbin model which includes both independent and dependent variables,then combine it with quantile regression model.This thesis proposes a spatial quantile Durbin model.which introduces instrumental variables to solve the endogenous problem of the model,and uses quantile method to estimate parameters.Furthermore,under Bayes theory,the parameter estimation of the spatial quantile Durbin model is studied,combining with the parameter priori.We can know the full conditional posterior distribution of parameters and study the sampling algorithm.In Chapter 2,We introduce the theoretical basis of the whole thesis.In Chapter 3,We build the proposed model and the specific estimation method of parameters.Under given assumptions,the consistency and asymptotic normality of parameter estimation are proved.In Chapter 4,we introduce the principle of combining Bayes method with quantile regression and study Bayesian analysis of spatial quantile Durbin model and study the sampling algorithm according to the characteristics of posterior distribution of parameters.Then,we obtain the MC estimation of parameters.Chapter 5 simulates the estimation method proposed in Chapter 3 and verifies the performance of the estimation method under finite samples.