Aggregate Kernel Inverse Regression Estimation

Abstract

Sufficient dimension reduction (SDR) is a useful tool for nonparametric regression with high-dimensional predictors. Many existing SDR methods rely on some assumptions about the distribution of predictors. Wang et al. proposed an aggregate dimension reduction method to reduce the dependence on the distributional assumptions. Motivated by their work, we propose a novel and effective method by combining the aggregate method and the kernel inverse regression estimation. The proposed approach can accurately estimate the dimension reduction directions and substantially improve the exhaustivity of the estimates with complex models. At the same time, this method does not depend on the arrangement of slices, and the influence of the extreme values of the response is reduced. In numerical examples and a real data application, it performs well.