Robust Dimension Reduction in Regression Using Divergences

• Activity Number: 161
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Tharuvai Sriram*+
• Companies: Univ of Georgia
• Keywords: Density divergences ; Dimension Reduction ; Regression ; Efficiency ; Robustness ; Tuning parameter

Abstract

Based on a rich family of divergences, we provide a sufficient dimension reduction approach in regression, which yields estimators that are inherently robust to data contamination. This family is shown to characterize the conditional independence underlying the concept of sufficient dimension reduction in regression. The novelty of our approach lies in exploiting the index of the family, which plays the role of a tuning parameter that balances the efficiency and the degree of robustness of our estimators. We discuss the detection of the true dimension and the selection of an optimal tuning parameter. More importantly, we assess robustness via influences functions and sample/empirical influence functions.