Aggregate Kernel Inverse Regression Estimation

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.

Automated summary

Sufficient dimension reduction (SDR) is a useful tool for nonparametric regression with high-dimensional predictors, but many existing SDR methods rely on certain assumptions about the distribution of predictors. In this study, inspired by Wang et al., we propose a novel and effective method that combines the aggregate method and the kernel inverse regression estimation. Our proposed approach accurately estimates the dimension reduction directions and substantially improves the exhaustivity of the estimates with complex models. It is not dependent on the arrangement of slices and reduces the influence of extreme values of the response. The method performs well in both numerical examples and a real data application.