Robust Group Identification and Variable Selection in Sliced Inverse Regression Using Tukey's Biweight Criterion and Ball Covariance

The SSIR-PACS is a group identification and model-free variable selection method under sufficient dimension reduction (SDR) settings. It combined the Pairwise Absolute Clustering Sparsity (PACS) with sliced inverse regression (SIR) methods to produce solutions sparsity ability of identification. However, depends on classical estimates for dispersion location, squared loss function, non-robust weights outliers. In this paper, robust version (RSSIR-PACS) proposed. We replaced by criterion Tukey's biweight. Also, outliers, which depend Pearson’s correlations, are substituted based recently developed ball correlation. Moreover, mean covariance matrix median covariance, respectively. RSSIR-PACS outliers in both response covariates. According results simulations, produces very good results. If existing, efficacy considerably better than competitors. addition, criteria estimate structural d makes practically feasible. we employed real data demonstrate utility RSSIR-PACS.