Abstract
The sliced inverse regression (SIR) is a technique for lowering the dimensions in regression applications without losing any information about the regression. Although the SIR has been demonstrated to be an effective strategy for dealing with high dimensional situations, it has the drawback of not containing all of the original predictors. By combining variable selection techniques with SIR, many researchers proposed solutions to this problem. One of these techniques combined the Elastic Net penalty with the SIR method (SIR-EN). The SIR-EN is an effective approach that does not rely on a parametric model. When the predictors are highly correlated under sufficient dimension reduction settings. However, SSIR- EN is not robust to outliers because it uses a loss function that is. As a result, we suggested RSSIR-EN as a robust version of SSIR-EN for outliers in both the dependent variable and the covariates.
