Robust inverse regression for dimension reduction

Sliced Inverse Regression for Dimension Reduction

Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach

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 regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspa...

An RKHS formulation of the inverse regression dimension-reduction problem

Suppose that Y is a scalar and X is a second-order stochastic process, where Y and X are conditionally independent given the random variables ξ1, . . . , ξp which belong to the closed span L 2 X of X. This paper investigates a unified framework for the inverse regression dimension-reduction problem. It is found that the identification of LX with the reproducing kernel Hilbert space of X provide...

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...

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...