Variable selection has been discussed under many contexts and especially, a large literature has been established for the analysis of right‐censored failure time data. In this article, we discuss an interval‐censored failure time situation where there exist two sets of covariates with one being low‐dimensional and having possible nonlinear effects and the other being high‐dimensional. For the problem, we present a penalized estimation procedure for simultaneous variable selection and estimation, and in the method, Bernstein polynomials are used to approximate the involved nonlinear functions. Furthermore, for implementation, a coordinate‐wise optimization algorithm, which can accommodate most commonly used penalty functions, is developed. A numerical study is performed for the evaluation of the proposed approach and suggests that it works well in practical situations. Finally the method is applied to an Alzheimer's disease study that motivated this investigation.

中文翻译：

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高维部分线性加性Cox模型的变量选择及其在阿尔茨海默氏病中的应用。

变量选择已在许多情况下进行了讨论，尤其是已经建立了大量文献来分析右删失时间数据。在本文中，我们讨论了一种间隔删失的故障时间情况，其中存在两组协变量，其中一组是低维的，并且可能具有非线性影响，而另一组是高维的。针对该问题，我们提出了同时选择和估计变量的惩罚估计程序，在该方法中，使用伯恩斯坦多项式来逼近所涉及的非线性函数。此外，为实现该功能，开发了一种可适应最常用惩罚函数的逐级优化算法。进行了数值研究，以评估所提出的方法，并表明该方法在实际情况下效果很好。最后，该方法被应用于阿尔茨海默氏病研究，从而激发了这一研究的热情。