Abstract The simultaneous estimation and variable selection for Cox model has been discussed by several authors when one observes right-censored failure time data. However, there does not seem to exist an established procedure for interval-censored data, a more general and complex type of failure time data, except two parametric procedures. To address this, we propose a broken adaptive ridge (BAR) regression procedure that combines the strengths of the quadratic regularization and the adaptive weighted bridge shrinkage. In particular, the method allows for the number of covariates to be diverging with the sample size. Under some weak regularity conditions, unlike most of the existing variable selection methods, we establish both the oracle property and the grouping effect of the proposed BAR procedure. An extensive simulation study is conducted and indicates that the proposed approach works well in practical situations and deals with the collinearity problem better than the other oracle-like methods. An application is also provided.

中文翻译：

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具有断裂自适应岭回归的区间删失数据的同时估计和变量选择

摘要 当观察右删失失效时间数据时，多位作者讨论了 Cox 模型的同时估计和变量选择。然而，除了两个参数程序外，似乎不存在用于区间删失数据的既定程序，这是一种更一般和更复杂的故障时间数据类型。为了解决这个问题，我们提出了一种结合了二次正则化和自适应加权桥收缩的优点的破碎自适应脊（BAR）回归程序。特别是，该方法允许协变量的数量随着样本大小而发散。在一些弱规律性条件下，与大多数现有的变量选择方法不同，我们建立了所提出的 BAR 程序的预言属性和分组效果。进行了广泛的模拟研究，并表明所提出的方法在实际情况下运行良好，并且比其他类似 oracle 的方法更好地处理共线性问题。还提供了一个应用程序。