title: Variable selection and estimation in generalized linear models with the seamlessL0penalty.
abstract: In this paper, we propose variable selection and estimation in generalized linear models using the seamlessL0(SELO) penalized likelihood approach. The SELO penalty is a smooth function that very closely resembles the discontinuousL0penalty. We develop an e cient algorithm to fit the model, and show that the SELO-GLM procedure has the oracle property in the presence of a diverging number of variables. We propose a Bayesian Information Criterion (BIC) to select the tuning parameter. We show that under some regularity conditions, the proposed SELO-GLM/BIC procedure consistently selects the true model. We perform simulation studies to evaluate the finite sample performance of the proposed methods. Our simulation studies show that the proposed SELO-GLM procedure has a better finite sample performance than several existing methods, especially when the number of variables is large and the signals are weak. We apply the SELO-GLM to analyze a breast cancer genetic dataset to identify the SNPs that are associated with breast cancer risk.
authors.affiliation: Department of Mathematics, Tsinghua University, Beijing China.
authors.forename: Zilin
authors.initials: Z
authors.lastname: Li
authors.forename: Sijian
authors.initials: S
authors.lastname: Wang
authors.forename: Xihong
authors.initials: X
authors.lastname: Lin
keywords: BIC; Consistency; Coordinate descent algorithm; Model selection; Oracle property; Penalized likelihood methods; SELO penalty; Tuning parameter selection