We propose a general dimension-reduction method that combines the ideas of likelihood, correlation, inverse regression and information theory. We do not require that the dependence be confined to particular conditional moments, nor do we place restrictions on the predictors or on the regression that are necessary for methods like ordinary least squares and sliced inverse regression. Although we focus on single-index regressions, the underlying idea is applicable more generally. Illustrative examples are presented.
Direction Estimation in Single-Index Regressions