Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions.We show that the recently proposed methods by Xia et al.(2002) can be 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.
|Place of Publication||Tilburg|
|Number of pages||26|
|Publication status||Published - 2005|
|Name||CentER Discussion Paper|
- Dimension reduction
- Nonparametric regression