Asymptotic properties of the maximum smoothed partial likelihood estimator in the change‐plane Cox model
研究了基于多个协变量分类的变化平面Cox模型，提出了最大平滑偏似然估计量，并证明了分类参数的收敛速度可接近n^{-1/2}（对数因子内），以及回归参数的渐近正态性。
Abstract 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 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.