Variable Selection and Estimation with Nonconvex Penalty Functions

• Activity Number: 299
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sijian Wang*+ and Zhigeng Geng and Grace Wahba
• Companies: University of Wisconsin, Madison and University of Wisconsin, Madison and Department of Statistics, University of Wisconsin - Madison
• Keywords: Penalized Estimation ; TCGA ; Variable Selection

Abstract

Variable selection and estimation via penalized least squares procedures have attracted great attention in recent literature. Based on continuous penalty functions, these methods simultaneously identify predictors associated with a given outcome and estimating their effects. In this talk, we present two novel nonconvex penalty functions: self-adaptive penalty and KSI-penalty. Both penalty functions reduce the estimation bias and improve the performance of variable selection and prediction. We explore the theoretical properties of the proposed methods. Simulation studies are conducted to demonstrate the proposed methods. We also apply the proposed methods to The Cancer Genome Atlas (TCGA) glioblastoma data.