Frailty Modeling and Penalized Likelihood Methodology

The penalized Gamma frailty model methodology of Fan and Li was extended in our previous papers to other frailty distributions. The penalty term was imposed on a generalized form of the likelihood function designed for clusters, which allows the direct use of many different distributions for the frailty parameter. In this paper, we discuss the asymptotic properties of the penalized likelihood estimators in shared frailty models. It is known that the rates of convergence depend on the tuning parameter which is involved in the penalty function. It is shown that with a proper choice of the tuning parameter and the penalty function, the penalized likelihood estimators possess an oracle property, namely, that they work as well as if the correct submodel was known in advance.