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.

翻译：变更平面Cox模型是生存数据亚组分析的常用工具。尽管该模型已有丰富文献，但有限维参数估计量的渐近性质研究仍十分有限。特别地，对于基于多个协变量进行分类的广义模型，其收敛速度乃至渐近分布尚未得到充分刻画。为弥补这一理论空白，本研究提出最大平滑部分似然估计量，并建立了以下渐近性质。首先，在协变量与调优参数选择的特定条件下，分类参数的收敛速度可逼近至1/n的对数阶。基于此收敛速度结果，本文进一步建立了回归参数的渐近正态性。