  The change-plane Cox model is a popular tool for the subgroup analysis of
survival data. Despite the rich literature on this model, there has been
limited investigation into the asymptotic properties of the estimators of the
finite-dimensional parameter. Particularly, the convergence rate, not to
mention the asymptotic distribution, has not been fully characterized 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 1/n up to a logarithmic factor under a certain condition on covariates
and the choice of tuning parameter. Given this convergence rate result, it also
establishes the asymptotic normality for the regression parameter.
