Robust Sliced Inverse Regression

Abstract

In this paper, two methods were suggested to make the estimations of Effective Dimension Reduction directions (E.D.R.-directions) robust in sliced inverse regression (SIR), through the robust estimate of the matrix of covariance, which depends upon the method, by using fast consistent high breakdown (FCH) and reweighted fast consistent high breakdown (RFCH) methods, we called the proposed methods (FCH-SIR) and (RFCH-SIR). Data has been contaminating by two types of outliers values which are asymmetric contamination (ACN) and symmetric contamination (SCN), and different contaminating ratios and sample sizes. Have been reached, through simulation experiments and real data. Conclusions showed that the two proposed methods in this paper gave better results compared to the ordinary SIR depending on the mean square errors (MSE) criterion for comparison.