Sliced inverse regression in reference curves estimation

Abstract

In order to obtain reference curves for data sets when the covariate is multidimensional, a new procedure is proposed. This procedure is based on dimension-reduction and non-parametric estimation of conditional quantiles. This semiparametric approach combines sliced inverse regression (SIR) and a kernel estimation of conditional quantiles. The asymptotic convergence of the derived estimator is shown. By a simulation study, this procedure is compared to the classical kernel non-parametric one for different dimensions of the covariate. The semiparametric estimator shows the best performance. The usefulness of this estimation procedure is illustrated on a real data set collected in order to establish reference curves for biophysical properties of the skin of healthy French women.