Robust Estimation of Dimension Reduction Space

Most dimension reduction methods based on nonparametric smoothing are highlysensitive to outliers and to data coming from heavy-tailed distributions. We showthat the recently proposed methods by Xia et al. (2002) can be made robust insuch a way that preserves all advantages of the original approach. Their extensionbased on the local one-step M-estimators is su±ciently robust to outliers and datafrom heavy tailed distributions, it is relatively easy to implement, and surprisingly,it performs as well as the original methods when applied to normally distributeddata.