Robust sufficient dimension reduction via α-distance covariance

Abstract

We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using α-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace is effectively estimated and model-free without estimating link function based on the projection on the Stiefel manifold. We establish the convergence property of the proposed estimation under some regularity conditions. We compare the performance of our method with existing SDR methods by simulation and real data analysis and show that our algorithm improves the computational efficiency and effectiveness.

Keywords:

• α-distance covariance
• central subspace
• sufficient dimension reduction (SDR)
• manifold learning
• robust statistics

Acknowledgments

The authors would like to thank the Editor, the Associate Editor and the reviewers for their constructive and insightful comments that greatly improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by NSF grants (DMS-1924792, DMS-2318925 and CNS-1818500).