A New Estimator for Efficient Dimension Reduction in Regression

• 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): Wei Luo* and Xizhen Cai
• Companies: Baruch College and Carnegie Mellon University
• Keywords: dimension reduction ; efficient estimation ; semiparametric regression ; variance estimation ; double-robustness property

Abstract

In this paper we propose a new estimator for efficient dimension reduction in regression, based on the work in Luo, Li and Yin (2014). Previous efficient estimators have been proposed by multiple authors, however under additional restrictive assumptions on the conditional variance of Y given X. These assumptions also complicate the implementation. In contrast, the new estimator employs no such assumptions, and thus is far more applicable and more convenient to use. By an extended double-robustness property, it reaches asymptotic efficiency under fairly general conditions. Its finite-sample effectiveness is further illustrated by simulation studies and a real data example.