Variable Selection and Shrinkage via a Conditional Likelihood-based Penalty

摘要

The usefulness of penalized regression to analyze large datasets is increasingly recognized, with a growing role in genome-wide association scans and in the analysis of data from other -omics technologies. Penalized regression has been applied to datain fields as diverse as health sciences, economics, and finance. We investigate connections between procedures to address "significance bias" or "winner's curse" in genome-wide association studies and the shrinkage of coefficient estimates and variableselection that is applied in existing penalized regression procedures. We use a conditional likelihood approach that has been applied to correct for significance bias in order to propose a new penalized regression procedure. The approach has a natural interpretation when the number of predictors is smaller than the sample size. In addition, we describe an analogous procedure when the number of predictors is larger than the sample size. We demonstrate via data examples and simulations that the procedureperforms favorably in terms of prediction error in both low-dimensional and high-dimensional settings in comparison to competing approaches, especially when the proportion of true nonzero coefficients is small.