Adaptive bridge estimator for Cox model with a diverging number of parameters

Abstract

This article considers the adaptive bridge estimator for Cox proportional hazards model with a diverging number of parameters. Specifically, we assume that the number of covariates of the Cox model is not fixed, and use the adaptive bridge penalty method to select variables and estimate the parameters of the Cox model. We show that under some weak regularity conditions, our proposed method has oracle properties and can select non-zero coefficients with a probability converging to 1. We also present an algorithm based on the Minorization-Maximization method to solve the adaptive bridge estimation. In addition, simulation studies show that the proposed method is effective and the well-known primary biliary cirrhosis data is provided to illustrate the application of the proposed method in survival problems.