Summary: Sliced Inverse Regression (S.I.R.) is a method for reducing the dimension of the explanatory variable in nonparametric regression problems. K. C. Li [J. Am. Statist. Assoc. 86, 316-342 (1991)] considers a general regression model of the form
with an arbitrary and unknown link function , and studies a link-free and distribution-free method for estimating , the space spanned by the ’s, called the effective dimension reduction (e.d.r.) space. It is widely applicable, easy to implement on a computer and requires no nonparametric smoothing devices such as kernel regression. The method begins with a partition of the range of into a fixed number of slices. Let us denote this partition. The conditional mean of given is then estimated by the sample mean within each slice.