Pseudo-Sufficient Dimension Reduction and Sufficient Variable Selection

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wenbo Wu*
• Keywords: correlated predictors ; dimension reduction ; measurement error regression ; ridge regression

Abstract

Sufficient dimension reduction has achieved great success in recent years. When the sample covariance matrix of the predictor vector is not invertible, many sufficient dimension reduction methods take an ad hoc ridge regression approach. A question that has been raised for a long while is whether the estimator of such an approach still belongs to the central subspace. In this expository paper, we propose a new concept of pseudo sufficient dimension reduction to answer this question. We uncover the underlying relationship between ridge regression and measurement error regression. With such a connection, we propose a general sufficient dimension reduction estimation procedure to obtain an estimate from a different subspace instead of the targeted population parameter space. Using an ensemble idea, our proposed pseudo estimate is better than the traditional estimate or a ridge estimate for highly correlated predictors, and avoids the difficulties for choosing a particular ridge tuning parameter. Our method requires no parametric assumptions on the underlying model. The effectiveness of the newly proposed methods are demonstrated by simulation studies and real data analyses.