Model Checks For Semiparametric Spatial Autoregressive Models Using Projections

We are in the age of information explosion,when facing massive information,how to deal with it is particularly important.Such as dealing with the unemployment rate,enrollment rate,disease infection rate and many others,it turns out that these types of data have spatial dependence or spatial autocorrelation.Ignoring these properties and adopting classical data analysis methods may lead to biased estimators and even contradict to the actual situations.Spatial autoregressive models are suitable to handle the spatial autocorrelation.However,the influence of some independent variables on response variables may be nonlinear in practical problems,which makes the models often possess linear and nonlinear structure at the same time.If the nonlinear effect is ignored and the linear spatial autoregressive model is adopted,the results of data analysis are often inappropriate even wrong.Therefore,the study of semiparametric spatial autoregressive model is necessary and has important theoretical research value and practical application value.In data analysis,one of the most important aspects is to verify the correctness of the fitted model.Since the adequation of a model affects the results of our research directly,performing model checking can provide basic supports for our statistical decision,improve the efficiency of modeling and save human and financial resources.In this dissertation,we consider the model checking for semiparametric spatial autoregressive models.First,B-splines are used to approximate the nonparametric components and then parameters are estimated via the generalized method of moments(GMM).It is proved that the estimators of the parametric and the nonparametric components have good asymptotic properties.Then,we propose the Cram?er-von Mises test statistics based on projection method using estimated residual errors.The asymptotic properties of the statistics are studied by means of empirical process under the null hypothesis and alternative hypothesis respectively.In order to determine the critical value of test statistics conveniently,a wild bootstrap method is proposed and relevant properties are studied.Finite sample properties are investigated via Monte Carlo simulations,illustrating the effectiveness of our proposed method.Finally,we apply this method to analyse the Boston housing price data and exhibit the practical usefulness of our proposed method.