Robust adaptive estimation of dimension reduction space - Pavel Čížek; Wolfgang Härdle (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2003)
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.
urn:nbn:de:kobv:11-10049716
Keywords: 330; nonparametric regression; dimension reduction; minimum average variance estimator; robust estimation; median absolute deviation; L1 regression; Nichtparametrisches Verfahren; Robustes Verfahren; Schätztheorie; Theorie