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This book is basically aiming to give a clear path to what one should do when facing outliers problem, especially in seemingly unrelated regression equations (SURE) models. Since the assumptions underlying most SURE estimators give little consideration to influential observations, which may be present in the dataset. It is well known that outliers in the data can severely influence classical estimators and their modifications; it may lead to the imprecision of these estimators, resulting in uncertainty when assessing the effects of the explanatory variables on the response variable. To overcome this problem, robust estimation is commonly applied to solve the problem caused by outliers. So, this book introduces a comparative study of some different robust estimators in SURE model. This is achieved by a simulation study and empirical application to evaluate the robust estimators. The Monte Carlo simulation and application results indicate that the (non-robust) ordinary least squares, maximum likelihood, and feasible generalized least squares estimators are very sensitive to outliers, while robust estimators are more effective, and give better performance than non-robust estimators.