variable selection and estimation in generalized linear models with the seamless {it l}_{{rm 0}} penalty精品.pdfVIP

The Canadian Journal of Statistics 745 Vol. 40, No. 4, 2012, Pages 745–769 La revue canadienne de statistique Variable selection and estimation in generalized linear models with the seamless L0 penalty 1 2 3 Zilin LI , Sijian WANG and Xihong LIN * 1Department of Mathematics, Tsinghua University, Beijing, China 2Department of Biostatistics Medical Informatics and Department of Statistics, University of Wisconsin, Madison, WI, USA 3Department of Biostatistics, Harvard University, Boston, MA, USA Key words and phrases: BIC; consistency; coordinate descent algorithm; model selection; oracle property; penalized likelihood methods; SELO penalty; tuning parameter selection. MSC 2010: Primary 62J07; secondary 62J12. Abstract: In this paper, we propose variable selection and estimation in generalized linear models using the seamless L0 (SELO) penalized likelihood approach. The SELO penalty is a smooth function that very closely resembles the discontinuous L0 penalty. We develop an efficient 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. The Canadian Journal of Statistic