Estimation Of Semiparametric Spatial Autoregressive Model With Missing Data

Spatial data usually has spatial dependencies,which makes the classical regression model based on the assumption of sample independence no longer applicable.Spatial econometric models describe the adjacency relationship between spatial individuals by introducing a spatial weight matrix,and are currently widely used in epidemiology,econometrics,ecology and other fields.Since the spatial relationship is often highly nonlinear,the semiparametric spatial models are more flexible and robust,which can make the estimation results more reliable than the linear spatial models.Most of the current literatures focus on the study of spatial models mainly assumes that there is no missing data,however,in practical application,due to various factors such as data temporarily unavailable or limited access technology,data missing is very common.For the problem of missing spatial data,the usual methods of dealing with missing values may not only destroy the structure of the spatial weight matrix,but also lose a lot of useful information.Therefore,the study of semiparametric spatial models under missing data has certain theoretical significance and practical value.In this thesis,we mainly study the estimation of the partial linear spatial autoregressive model with the response variable missing at random,the Expectation Maximization(EM)algorithm for solving the Maximum Likelihood(ML)estimation of the model,the EM algorithm for Pseudo Restricted Maximum Likelihood(PREML)estimation and the Marginal Maximum Likelihood(MML)algorithm for MML estimation are given respectively,in which the unknown smooth function is approximated by Bspline method.The PREML estimation is mainly used to correct the estimate bias of the variance parameter,while the MML method avoids the iterative process of the EM algorithm by directly maximizing the observed log-likelihood function.In addition,numerical simulations under different settings show that the three estimation methods are all significantly better than the quasi-likelihood method,and each has its own advantages.The EM algorithm for PREML estimation is suitable for estimating the error variance parameter,and the EM algorithm for ML estimation is more suitable for estimating other parameters and nonparametric parts of the model.Although the estimation accuracy of the MML method is slightly inferior to that of the EM algorithm for ML estimation,its calculation speed is much faster than the first two methods,especially when the missing ratio is large.Finally,the effectiveness of the three estimation methods are verified by a real data analysis.