Non-parametric estimation of direction in single-index models with categorical predictors

This paper proposes a general dimension-reduction method targeting the partial central subspace recently introduced by Chiaromonte, Cook & Li. The dependence need not be confined to particular conditional moments, nor are restrictions placed on the predictors that are necessary for methods like partial sliced inverse regression. The paper focuses on a partially linear single-index model. However, the underlying idea is applicable more generally. Illustrative examples are presented.