When the number of variables is large, regression analysis is a difficult process in the sense that increasing the number of variables contributes to increasing the complexity of the model and this may lead to the problem of the dimensionality curse, and this problem prompted researchers to work to reduce these high dimensions of the data, and there are two ways to reduce the dimensions, which is the method of choosing Variables (V.S) and Variables extractions. Under the assumptions of the SDR (Sufficient dimension reduction) theory, the researchers also worked on proposing methods to reduce dimensions, including merging SDR methods with regularization methods, and among these methods (SMAVE-AdEN (Alkenani and Rahman) (2020), which is a method for selecting a variable under assumptions The SDR theory, and the SMAVE-AdEN method is a result of the combination of Adaptive elastic net method and (MAVE) (Minimum average variance estimator) method for estimating minimum average variance. to estimate the average minimum variance. This method is effective when the variables are highly correlated, but the SMAVE-AdEN method is not robust and is a sensitive method that is affected when there are outliers in the data, because it uses the least squares criterion. Here we propose a robust method for variable selection under SDR assumptions called (RSMAVE-AdEN). It is not affected by outliers found in both the explanatory and response variables. The efficiency of the proposed method was verified by studying and analyzing real data of diabetic patients.

dimensionality reduction, RSMAVE-AdEN, sparsely robust adaptive elastic network, MAVE method.