In regression applications, the sliced inverse regression(SIR) is a method for reducing the dimensions without losing any information about the regression. Although, the SIR has been proven as an efficient method to deal with the high dimensionality problems, but it suffers that it gives directions contains all the original predictors. Many researchers suggested approaches to dealing with this problem by combining variable selection methods with SIR. One of these methods combined the SIR method with Elastic Net penalty(SIR-EN). The SIR –EN is an efficient method without assuming a parametric model. It produces accurate and sparse solutions when the predictors are highly correlated under sufficient dimension reduction settings. However, the SSIR- EN is not robust to outliers because of the method use the loss function which is sensitive to outliers in data. As a result, we suggested RSSIR-EN as a robust version of SSIR-EN for outliers in both the dependent variable and the covariates.

Dimension reduction, SIR, Robust estimation, Elastic-Net.