Estimation For Semi-parametric Regression Models With Spatial Data

The data collected in practice often has geospatial attributes.Data with spatial coordinates or relative positions are collectively referred to as spatial data,and there is a certain correla-tion between these spatial data.Statistical analysis of spatial data has always been a research hotspot in statistics and econometrics.Therefore,this thesis considers the statistical inference of semi-parametric models with spatial geographical markers,which has important theoretical significance and valueThis thesis focuses on the estimation of spatial models when ?(Yi,Xi,Zi),i E GN} sat-isfies the strong mixing condition,including the estimation of parameters and non-parameters Parametric component estimators are obtained by least square method on the basis of tensor product B-splines functions approximating multivariate nonparametric functions.For the non-parametric part,the local mode kernel estimation method based on B-splines is used to estimate the coefficients corresponding to the approximation function after the parameter component es-timator is substituted back into the model.Then the asymptotic normality of the parameter component estimator and the convergence rate and asymptotic normality of parametric coeffi-cient estimators of nonparametric components are given and proved under given assumptions And the spatial block technique is used in the main proof of the results.In chapter 4,the thesis introduces a kind of semi-parametric space lag model.Compared with the model avoiding any parametric specification of the possibly extremely complex spatial dependent structure of the data in chapter 3,the semi-parametric space lag model introduces the space weight matrix and space lag factor and so as to further broaden the scope of model analysisFinally,Monte Carlo simulation is used to investigate the performance of the proposed method under five different error distributions.The results show that compared with the least squares estimation,our method is more effective and robust to estimate the nonparametric com?ponent of model when the data has outliers or the error is not normally distributed.