Robust Estimation Of Semi-Functional Partial Linear Spatial Autoregressive Model

With the development of science and technology,the collection and storage of realtime data,such as continuously recorded temperature and rainfall data,has become more and more convenient,which makes functional data analysis become a research hotspot in the field of statistics in recent years.Regression analysis is an important research content in functional data analysis.Existing functional regression models often assume that the data are independent of each other,but do not consider the possible spatial dependence structure between observed data.Meanwhile,the general model estimation methods(such as least squares and maximum likelihood estimation)are not robust enough when the data contains outliers.Therefore,it has some theoretical significance and application value to study the robust estimation of functional regression models in the case of spatial dependence.Aiming at the possible existence of spatially dependent structure and outliers in the data,this dissertation studies the robust estimation of semi-functional partial linear spatial autoregressive models.Specifically speaking,based on local linear estimation,two-stage least squares estimation and quasi maximum likelihood estimation,two-stage robust estimation and robust likelihood estimation are proposed,and the effectiveness of the proposed robust estimation is verified by simulation research and empirical analysis.The results show that when the error term obeys the normal distribution,the effect of quasi maximum likelihood estimation and two-stage least squares estimation is close.However,the robust estimation methods proposed in this dissertation perform well when the error term obeys the mixed normal distribution and distribution.In addition,although the results of robust quasi likelihood estimation are slightly better than two-stage robust estimation,the calculation speed of two-stage robust estimation is faster.Finally,the model is used to analyze the meteorological data of Spain,and the empirical results also prove that the robust estimation proposed in this dissertation is effective.