Reference curve estimation via alternating sliced inverse regression

In order to obtain reference curves for data sets when the variable of interest and the covariate are multidimensional, we propose a new methodology in this article based on a dimension-reduction approach and non-parametric estimation of conditional quantiles. This approach is semiparametric and combines Alternating Sliced Inverse Regression and a kernel estimation of conditional quantiles. The usefulness of this estimation procedure is illustrated with a real data set collected for the purpose of establishing reference curves for the biophysical properties of the skin of healthy French women. Copyright © 2003 John Wiley & Sons, Ltd.