Sufficient dimension reduction via distance covariance with multivariate responses

ABSTRACT

In this article, we propose a new method for sufficient dimension reduction when both response and predictor are vectors. The new method, using distance covariance, keeps the model-free advantage, and can fully recover the central subspace even when many predictors are discrete. We then extend this method to the dual central subspace, including a special case of canonical correlation analysis. We illustrated estimators through extensive simulations and real datasets, and compared to some existing methods, showing that our estimators are competitive and robust.

KEYWORDS:

• Central subspace
• distance covariance
• dual central subspace
• projective resampling
• sufficient dimension reduction

Acknowledgments

The authors would like to thank the Editor, an Associate Editor and two referees for their valuable comments and suggestions, which lead to a greatly improved paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Yin's research was supported in part by National Science Foundation (Directorate for Computer and Information Science and Engineering) Grant CIF-1813330.