Best subset selection with shrinkage: sparse additive hazards regression with the grouping effect

Sparse modeling plays a ubiquitous role in modern statistical regression. In particular, high-dimensional survival analysis has drawn a lot of attention as a result of the popularity of microarray studies involving survival data. In this paper, we focus on a scenario where predictors are strongly correlated, also known as grouping effect, which is highly desirable when analysing high-dimensional microarray data. To perform simultaneous variable selection and estimation under this circumstance, we propose the l(2)-regularized best-subsets estimator under the framework of additive hazards models based on a polynomial algorithm for the best subset selection. Moreover, we establish comprehensive statistical properties, including oracle inequalities under estimation loss for the proposed estimator. The proposed method is demonstrated by simulation studies and illustrated by a real data example.