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...

The basic ideas of Desirability functions and indices are introduced and compared to other methods of multivariate optimisation. It is shown that gradient based techniques are not in general appropriate to perform the numerical optimisation for Desirability indices. The problems are shown for...

Sliced inverse regression (SIR) is a clever technique for reducing the dimension of the predictor in regression problems, thus avoiding the curse of dimensionality. There exist many contributions on various aspects of the performance of SIR. Up to now, few attention has been paid to the problem...

We propose multivariate classification as a statistical tool to describe business cycles. These cycles are often analyzed as a univariate phenomenon in terms of GNP or industrial net production ignoring additional information in other economic variables. Multivariate classification overcomes...