Variable Selection and Shrinkage via a Conditional Likelihood-Based Penalty

• Activity Number: 182
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Arpita Ghosh*+ and Fred Wright and Andrew Nobel and Fei Zou
• Companies: National Cancer Institute and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: variable selection ; shrinkage ; penalized regression ; conditional likelihood ; winner's curse

Abstract

The usefulness of penalized regression to analyze large data sets is increasingly recognized, with a growing role in genome-wide association scans and in the analysis of data from other -omics technologies. We investigate the potential connections between correction procedures for "winner's curse" in genome wide association studies with the shrinkage of coefficient estimates and variable selection that is applied in existing penalized regression procedures. We use a conditional likelihood approach that has been applied to correct for winner's curse in order to propose a new penalized regression procedure. We describe an analogous procedure when the number of predictors is larger than the sample size. We demonstrate via simulation that the procedure has favorable prediction error in comparison to competing approaches, especially when the proportion of true nonzero coefficients is small.