Response dimension reduction: model-based approach

ABSTRACT

In this paper, a model-based approach to reduce the dimension of response variables in multivariate regression is newly proposed, following the existing context of the response dimension reduction developed by Yoo and Cook [Response dimension reduction for the conditional mean in multivariate regression. Comput Statist Data Anal. 2008;53:334–343]. The related dimension reduction subspace is estimated by maximum likelihood, assuming an additive error. In the new approach, the linearity condition, which is assumed for the methodological development in Yoo and Cook (2008), is understood through the covariance matrix of the random error. Numerical studies show potential advantages of the proposed approach over Yoo and Cook (2008). A real data example is presented for illustration.

KEYWORDS:

• Envelope
• Grassmann manifold
• multivariate regression
• response dimension reduction
• sufficient dimension reduction

AMS SUBJECT CLASSIFICATION:

• 62G08
• 62H05

Acknowledgements

The author Jae Keun Yoo is grateful to the associate editor and the three referees for many insightful and helpful comments. Also, the author appreciates Professor Thomas Richardson (Chair, Department of Statistics, University of Washington, USA) to provide many significant and insightful comments to finalize the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

For Jae Keun Yoo, 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-2012R1A1A1040077 and 2009-0093827].