Aggregate Inverse Mean Estimation for Sufficient Dimension Reduction

Abstract

Abstract–Many well-known sufficient dimension reduction methods investigate the inverse conditional moments of the predictors given the response. The required linearity condition, the number and arrangement of slices, and the inability to detect symmetric dependence are among several long-standing issues that have negatively impacted on the use of these approaches. Motivated by two recent works dealing with the choice of number of slices, we propose a novel and effective method based on the aggregation of inverse mean estimation. The new approach can substantially improve the estimation accuracy, break down the symmetry to achieve exhaustive estimation, and is much less sensitive to the violation of the linearity condition. Both simulation studies and a real data application show the efficacy of the newly proposed approach.

Keywords:

• Aggregate inverse mean estimation
• Central subspace
• Cumulative mean estimation
• Sliced inverse regression
• Sufficient dimension reduction

Supplementary Materials

Additional simulation results: Detailed simulation results included as a pdf file.

R code: The zip file contains R program code to perform the AIME method described in the article.

Acknowledgments

We are grateful to the editor, an associate editor, and three reviewers for their helpful comments and constructive suggestions on an earlier version of the article, which lead to a significant improvement of this article.

Additional information

Funding

Yin’s work is supported in part by an NSF grant CIF-1813330.