Summarizing the effect of many covariates through a few linear combinations is an effective
way of reducing covariate dimension and is the backbone of (sufficient) dimension …

Sufficient dimension reduction is a rapidly developing research field that has wide
applications in regression diagnostics, data visualization, machine learning, genomics …

We introduce directional regression (DR) as a method for dimension reduction. Like contour
regression, DR is derived from empirical directions, but achieves higher accuracy and …

A family of dimension-reduction methods, the inverse regression (IR) family, is developed by
minimizing a quadratic objective function. An optimal member of this family, the inverse …

We provide a novel and completely different approach to dimension-reduction problems
from the existing literature. We cast the dimension-reduction problem in a semiparametric …

In this paper we propose a dimension reduction method for estimating the directions in a
multiple-index regression based on information extraction. This extends the recent work of …

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient
dimension reduction. In parallel to the classical slicing estimation, we develop three …

We obtain the maximum likelihood estimator of the central subspace under conditional
normality of the predictors given the response. Analytically and in simulations we found that …

Dimension reduction for regression is a prominent issue today because technological
advances now allow scientists to routinely formulate regressions in which the number of …

Existing sufficient dimension reduction methods suffer from the fact that each dimension
reduction component is a linear combination of all the original predictors, so that it is difficult …