Variable Selection in Partially Linear Additive Hazards Model with Grouped Covariates and a Diverging Number of Parameters

• Activity Number: 152 - Frontiers of High-Dimensional and Complex Data analysis
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Xuewen Lu* and Arfan Afzal
• Companies: University of Calgary and University of Calgary
• Keywords: Additive hazards model; bi-level variable selection; censored data; hierarchical penalty; partially linear model; survival analysis

Abstract

In this talk, we introduce group variable selection in the partially linear additive hazards (AH) model with right censored data. We assume a grouping structure exists among the high-dimensional linear explanatory variables in the presence of nonparametric risk functions of low-dimensional covariates. We propose a hierarchical bi-level variable selection approach for group selection and individual variable selection within groups. The proposed methods are capable of simultaneously conducting estimation and bi-level variable selection. The rate of convergence of the parameter estimators is derived and the selection consistency is obtained under a hierarchical penalty and an adaptive hierarchical penalty, respectively. Finally, computational algorithms and programs are developed for utilizing the proposed methods. Simulation studies indicate good finite sample performance of the methods. Real data examples are provided to illustrate the application of the methods.