Asymptotic Properties of the Maximum Smoothed Partial Likelihood Estimator in the Change-Plane Cox Model

The change-plane Cox model is a popular tool for the subgroup analysis of the survival data. Despite the rich literature on this model, there has been limited investigation on the asymptotic properties of the estimators of the finite dimensional parameter. Particularly, the convergence rate, not to mention the asymptotic distribution, remains an unsolved problem for the general model where classification is based on multiple covariates. To bridge this theoretical gap, this study proposes a maximum smoothed partial likelihood estimator and establishes the following asymptotic properties. First, it shows that the convergence rate for the classification parameter can be arbitrarily close to n^-1 up to a logarithmic factor, depending on a choice of tuning parameter. Second, it establishes the asymptotic normality for the regression parameter.