Robust estimation of dimension reduction space

Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions. Two recently proposed methods, minimum average variance estimation and outer product of gradients, can be and are made robust in such a way that preserves all advantages of the original approach. Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy-tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data. (c) 2005 Elsevier B.V. All rights reserved.