On Some Extensions Of Robust Estimators In Spatial Autoregressive Models

In the past decades,the data collection techniques have been developed exten-sively and the growing needs for analyzing the spatial data have largely stimulated the corresponding studies in statistics and econometrics.The spatial data are expose to potential correlation structure and traditional linear models cannot accommodate this type of information appropriately.Spatial autoregressive models are designed targeted to capturing such spatial dependence and have been extensively studied in recent years.However,as in many field of statistical research,outliers are unavoidable in spatial data analysis and the presence of outlying observations tend to impact the performance of maximum likelihood estimator and lead to misleading conclusions.In current the-sis,we employ Tukey's robust loss function to modify the conventional maximum likelihood estimator and we aim to reduce the influence of outlying observations.The robustified likelihood function is developed accordingly.We provide the robustified score functions and based on which the Fisher scoring algorithm is also developed.Monte Carlo simulations are employed to assess the performance of our proposed ro-bust estimation method.The results show that in comparison to conventional maximum likelihood estimator,the proposed Tukey-type robust estimator and existing Huber-type robust estimator lead to very comparable performance when there are no outliers.In addition,when the data are contaminated by outliers,the robust estimation methods typically lead to smaller bias and better mean square error.We also find that our pro-posed Tukey-type robust estimator tends have better performance over its counterpart based on Huber's rho function in estimating the spatial autoregressive coefficient.Two case studies are adopted to illustrate the use of our robust estimation method and the results further support the use of Tukey-type robust estimator in practical situations.