To overcome the curse of dimensionality, dimension reduction is important andnecessary for understanding the underlying phenomena in a variety of fields.Dimension reduction is the transformation of high-dimensional data into ameaningful representation in the low-dimensional space. It can be...

Sliced Inverse Regression (SIR) is a promising technique for the purpose of dimension reduction. Several properties of this relatively new method have been examined already, but little attention has been paid to robustness aspects. We show that SIR is very sensitive towards outliers in the data....

In the common nonparametric regression model with high dimensional predictor several tests for the hypothesis of an additive regression are investigated. The corresponding test statistics are either based on the diiferences between a fit under the assumption of additivity and a fit in the...