Robust Estimation Of Partial Linear Spatial Autoregressive Model Based On Quantile Regression And Its Application

As an extension of traditional econometric models,spatial autoregressive models have been widely used in economics,social sciences,geographical sciences and other fields,and many scholars have incorporated spatial lag into the model for analysis,thereby obtaining a more comprehensive interpretation of the dependent variable.As a kind of semiparametric model,partial linear model divides covariates into parametric terms and non-parametric terms for regression,which effectively solves the problem of dimensional calamity in nonparametric regression,so a large number of scholars have studied the properties of partial linear models.In this thesis,the spatial autoregressive model is combined with a partial linear model to construct a partial linear spatial autoregressive model,which further expands the scope of application of the model.Considering that quantile regression can more comprehensively display the distribution characteristics of dependent variables than mean reversion,this thesis considers the robust estimation and asymptotic nature of some linear spatial autoregressive models under longitudinal data and missing data based on quantile regression method,and puts forward corresponding countermeasures and suggestions for the research and analysis of per capita GDP of some cities in the Chengdu-Chongqing Economic Circle based on the method of this thesis.Firstly,the robust estimation of some linear spatial autoregressive models under longitudinal data is considered.Firstly,the B-spline method is used to approximate the non-parametric terms in the model,and the parameters are estimated by selecting appropriate tool variables and using the instrumental variable adjustment method.Then,under some regular conditions,a proof of the asymptotic nature of the estimator is given;Finally,considering the simulation of the estimator,the instrumental variable adjustment method,least squares estimation method and traditional quantile regression method are compared based on different quantile points,and the results show that the estimator based on the instrumental variable adjustment method is more robust.Then,consider the robust estimation of partial linear spatial autoregressive models under the missing data.Firstly,the data deletion mechanism is defined as random deletion,and the pairwise deletion method is used to consider the statistical analysis under the complete observation data.Then,the B-spline method is used to approximate the non-parametric terms in the model,and the parameters under the complete observation data are estimated by selecting the appropriate tool variables,and the instrumental variable adjustment method is used to estimate the parameters under the complete observation,and the missing values are linearly imputed.Finally,under some regular conditions,the asymptotic property proof of the estimator based on the complete observation data and the asymptotic property proof of the estimator under the imputed data are given,and the simulation study is carried out to consider the parameter estimation under different missing data,and the results show that the accuracy of the estimation is improved by linear imputation.Finally,the method of this thesis is considered to be applied to the per capita GDP study of some cities in the Chengdu-Chongqing Twin Cities Economic Circle.Firstly,the indicators were screened and integrated,and the rationality of the selected indicators was analyzed,and a complete index system was constructed.Then,partial linear spatial autoregressive model is used to model the corresponding index,and the estimated value of the parameter is obtained based on the tool variable adjustment method in this thesis,and the results are analyzed.Finally,according to the analysis results,corresponding policy suggestions are given.