The use of random-effect models for high-dimensional variable selection problems

We study the use of random-effect models for variable selection in high-dimensional generalized linear models where the number of covariates exceeds the sample size. Certain distributional assumptions on the random effects produce a penalty that is non-convex and unbounded at the origin. We introduce a unified algorithm that can be applied to various statistical models including generalized linear models. Simulation studies and data analysis are provided.