Dimension reduction via parametric inverse regression

In this paper, a linear subspace containing part or all of the information for the regression of a m-vector Y on a p-vector X and its dimension are estimated via the means of inverse regression. Smooth parametric curves are fitted to the p inverse regressions through a multivariate linear model, without imposing any strict assumptions on the error distribution. This method is expected to be more powerful in reducing the dimension of a regression problem when compared to SIR, the estimation procedure proposed by Li (1991), that is based on fitting piecewise constant functions to the inverse regression curves.