On surrogate dimension reduction for measurement error regression: An invariance law

Sliced Regression for Dimension Reduction

By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is free of the linearity condition (Li, 1991) and enjoys much improved estimation accuracy. Compared wit...

Regression on manifolds using kernel dimension reduction

We study the problem of discovering a manifold that best preserves information relevant to a nonlinear regression. Solving this problem involves extending and uniting two threads of research. On the one hand, the literature on sufficient dimension reduction has focused on methods for finding the best linear subspace for nonlinear regression; we extend this to manifolds. On the other hand, the l...

Sliced Inverse Regression for Dimension Reduction

Gradient-based kernel dimension reduction for regression

This paper proposes a novel approach to linear dimension reduction for regression using nonparametric estimation with positive definite kernels or reproducing kernel Hilbert spaces. The purpose of the dimension reduction is to find such directions in the explanatory variables that explain the response sufficiently: this is called sufficient dimension reduction. The proposed method is based on a...

Minimax adaptive dimension reduction for regression

In this paper, we address the problem of regression estimation in the context of a p-dimensional predictor when p is large. We propose a general model in which the regression function is a composite function. Our model consists in a nonlinear extension of the usual sufficient dimension reduction setting. The strategy followed for estimating the regression function is based on the estimation of ...