The elimination of insignificant predictors and the combination of predictors with indistinguishable coefficients are the two issues raised in searching for the true model. Pairwise Absolute Clustering and Sparsity (PACS) achieves both goals. Unfortunately, PACS is sensitive to outliers due to its dependency on the least-squares loss function which is known to be very sensitive to unusual data. In this article, the sensitivity of PACS to outliers has been studied. Robust versions of PACS (RPACS) have been proposed by replacing the least squares and nonrobust weights in PACS with MM-estimation and robust weights depending on robust correlations instead of person correlation, respectively. A simulation study and two real data applications have been used to assess the effectiveness of the proposed methods.

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In this paper the authors propose a group-lasso for sliced inverse regression (group lasso-SIR). This proposed method can deal with the problem of correlation existence between predictor variables. Simulation is used to investigate the performance of proposed method comparing with ridge and lasso in sliced inverse regression (lasso-SIR). The results show that the group lasso-SIR method is performs well comparing with other methods depending on Mean Square Errors (MSE) criterion.