On Gaussian Oracle Inequalities for Structured Selection in Nonparametric Cox Model

• Activity Number: 613
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jelena Bradic*+ and Rui Song
• Companies: UC San Diego and North Carolina State University

Abstract

In this paper we propose a general class of group penalties suitable for sparse structured variable selection and estimation in the context of high dimensional nonparametric Cox proportional hazard's model. We study the finite sample oracle prediction bounds and exemplify differences between bounded and unbounded non-parametric covariate effect. In particular, we show how unbounded effects lead to possibly larger prediction bounds. Moreover, we propose a sequence of sparse non-convex group regularizations and show when is group Scad penalty preferred to group Lasso. Hierarchical and smoothed variable selection in Cox model are also discussed as two special cases of the proposed general framework.