We consider a Cox-type regression model with change-points in the covariates. A change-point specifies the unknown threshold at which the influence of a covariate shifts smoothly, i.e., the regression parameter may change over the range of a covariate and the underlying regression function is continuous but not differentiable. The model can be used to describe change-points in different covariates but also to model more than one change-point in a single covariate. Estimates of the change-points and of the regression parameters are derived and their properties are investigated. It is shown that not only the estimates of the regression parameters are square root n-consistent but also the estimates of the change-points in contrast to the conjecture of other authors. Asymptotic normality is shown by using results developed for M-estimators. At the end of this paper we apply our model to an actuarial dataset, the PBC dataset of Fleming and Harrington (Counting processes and survival analysis, 1991) and to a dataset of electric motors.

中文翻译：

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协变量中有变化点的 Cox 型回归模型。

我们考虑在协变量中有变化点的 Cox 型回归模型。变化点指定协变量的影响平滑移动的未知阈值，即回归参数可能在协变量的范围内变化，并且潜在的回归函数是连续的但不可微的。该模型可用于描述不同协变量中的变化点，也可用于对单个协变量中的多个变化点进行建模。导出变化点和回归参数的估计并研究它们的特性。结果表明，与其他作者的猜想相反，不仅回归参数的估计是平方根 n 一致的，而且变化点的估计也是如此。通过使用为 M 估计量开发的结果显示渐近正态性。