Non-Parametric Estimation of Direction in Single-Index Models With Categorical Predictors

Abstract

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.

Sufficient dimension reduction and variable selection for regression mean function with two types of predictors

“…Pooled estimate doesn't select WCC, because it only has very weak effect in female group and has no effect in male group, while the pooled estimator is more focusing on common informative variables. The results of Chiaromonte et al (2002) and Yin (2005) are similar in terms of estimating dimension reduction subspaces but without variable selection.…”

“…We are interested in the relationship between an athlete's lean body mass(LBM) and six covariates, height, weight, red cell count, white cell count, hemoglobin, plus an indicator for gender. The same problem has been studied by Chiaromonte et al (2002) and Yin (2005). We apply sparse MAVE to the male group and the female group separately, and also the two-step procedure.…”

Estimating Directions in Extending Generalized Partially Linear Single-Index Models

“…In Section 3.1, we suggest a new method that is based on information theory extending from Yin and Cook (2005) and Yin (2005) to the case with two sets of predictors. In Section 3.2, we propose an actual algorithm, and some asymptotic theory will be discussed in Section 3.3.…”

“…where the second term is not related to α α α, while the first part is used by Yin (2005) to recover the index for a partial single-index model in a partial CS, S W Y |X . Thus, we can view this method as a natural way extending from estimating marginal CS and partial CS to joint CS.…”

A review on the generalization of sufficient dimension reduction methods with the additional information

“…In this framework, W is treated as another covariate without entering the process of dimension reduction. Yin shows that , which gives a general inclusion property for these subspaces. Because W may not be available all the time, the target of interest in this study focuses on instead of nor .…”