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Čížek, Pavel
Härdle, Wolfgang
Year of Publication: 
Series/Report no.: 
SFB 373 Discussion Paper 2003,1
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 MAVE and OPG methods by Xia et al. (2002) allow us to make them robust in a relatively straightforward way that preserves all advantages of the original approach. The best of the proposed robust modifications, which we refer to as MAVE-WMAD-R, is sufficiently robust to outliers and data from heavy tailed distributions, it is easy to implement, and surprisingly, it also outperforms the original method in small sample behaviour even when applied to normally distributed data.
nonparametric regression
dimension reduction
minimum average variance estimator
robust estimation
median absolute deviation
L1 regression
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Working Paper

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