Groupwise Sufficient Dimension Reduction via Envelope Method

• Activity Number: 75
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Zifang Guo*+ and Lexin Li and Wenbin Lu
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Central subspace ; Direct sum envelope ; Groupwise dimension reduction

Abstract

In many dimension reduction problems, the predictors come from different groups, and it is often desirable to incorporate such prior group information into dimension reduction procedures to obtain more informative and more interpretable estimates. In this article, we propose a groupwise dimension reduction method which aims to recover full regression information in the conditional distribution of response given the predictors, while preserving the group structure of the predictors. The proposed method is based on imposing a group structure onto classical central subspace estimators via a direct sum envelope. Simulation studies and real data analysis show that the proposed method achieves competent nite sample performance, in terms of both estimation accuracy and interpretability of the resulting estimator.