Robust Weighted Least Squares Method using different schemes of M-estimators (RWLSM), A comparative Study

In this research, it was reducing or excluding the effect of not satisfying the assumption of normal distribution of the data, due to the presence of types of outlying values in it when we wish to choose the best regression equation by robust methods, and this was achieved by introducing weights from the robust methods in the estimate and testing their robustness and suitability for the model in advance, And then selecting the weights resulting from the highest efficient robust methods and introducing these weights in the stages of selecting best regression equation, which results in a model that achieves two characteristics at the same time, which are robustness and reducing dimensions in return for increasing efficiency.The simulation approach was used on models with different dimensions, different sample sizes, and different contamination rates in the dependent variable once, in the independent variables again, and in both together, with a focus on studying the possible impact of the presence of outliers on the variables that will remain in the model and the variables that will be deleted. .To achieve the idea of the paper, a number of robust estimation methods were studied, and the results were compared with the ordinary least squares method (OLS) and the robust adaptive LASSO method on experimental data using simulation, as well as on data for a sample of thalassemia patients in Nineveh province..