Marginal Empirical Likelihood and Sure Independence Feature Screening

• Activity Number: 361
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jinyuan Chang*+ and Cheng Yong Tang and Yichao Wu
• Companies: Peking University and University of Colorado Denver and NC State University
• Keywords: Empirical likelihood ; high dimensional data analysis ; independence sure screening ; large deviation

Abstract

We study a marginal empirical likelihood approach when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear regression models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, our approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions.