Sufficient dimension reduction through informative predictor subspace

Abstract

The purpose of this paper is to define the central informative predictor subspace to contain the central subspace and to develop methods for estimating the former subspace. Potential advantages of the proposed methods are no requirements of linearity, constant variance and coverage conditions in methodological developments. Therefore, the central informative predictor subspace gives us the benefit of restoring the central subspace exhaustively despite failing the conditions. Numerical studies confirm the theories, and real data analyses are presented.

Keywords:

• central subspace
• informative predictor subspace
• linearity condition
• regression
• sufficient dimension reduction

AMS Subject Classification:

• 62G08
• 62H05

Acknowledgments

The author is grateful to the associate editor and the two referees for many insightful and helpful comments. Also, the author appreciates the Department of Statistics, University of Washington, to provide a comfortable research environment during the visit in 2016. The author gives a special thank to Hye Yeon Um to help to finish this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (NRF-2014R1A2A1A11049389/2009-0093827).