Nearest neighbor inverse regression

Sliced inverse regression (SIR), formally introduced by Li, is a very general procedure for performing dimension reduction in nonparametric regression. This paper considers a version of SIR in which the slices are determined by nearest neighbors and the response variable takes value possibly in a multidimensional space. It is shown, under general conditions, that the effective dimension reduction space can be estimated with rate n -1/2 where n is the sample size.