Robust estimation approach for spatial error model

Spatial regression models, used to model spatial relationships, have received considerable attention in recent years since numerous data sets have been collected with geographical references in space. The spatial error model (SEM), among spatial regression models, has been widely applied for spatial data in the literature due to its simple structure. However, it is known that the classical estimation methods such as the maximum likelihood and generalized moment can be influenced by the presence of outliers in the data. In this article, a robust estimation approach based on the robustified likelihood equations for SEM is proposed. The results of the simulation study show that the proposed estimator for SEM has smaller bias and mean squared errors and exhibits more robust empirical influence function than the classical methods, when there are outliers in the dataset. The results of all analysis show that the proposed estimator is robust to outliers.