A note on the choice of the number of slices in sliced inverse regression

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 of choosing the number of slices within the SIR procedure appropriately. The aim of this paper is to show that especially the estimation of the reduced dimension can be strongly in?uenced by the chosen number of slices.