We propose a projection-based cross-validation method for estimating a low-dimensional parameter in the presence of a high-dimensional nuisance parameter in the Cox regression model. We show that the proposed estimator is asymptotically normal, which enables us to conduct hypothesis test for the parameter of interest with high-dimensional nuisance parameters. Three decision rules are presented to avoid the influence of random splitting of samples. Simulation studies indicate that our method is more powerful than that of Fang et al. (2017, JRSSB) when the coefficients of predictors are high-dimensional and not very sparse. As an illustrative example, we apply our procedure to a breast cancer study.

中文翻译：

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高维 Cox 模型中基于投影和交叉验证的估计

我们提出了一种基于投影的交叉验证方法，用于在 Cox 回归模型中存在高维有害参数的情况下估计低维参数。我们表明，所提出的估计量是渐近正态的，这使我们能够对具有高维有害参数的感兴趣参数进行假设检验。为了避免样本随机分裂的影响，提出了三种决策规则。模拟研究表明，我们的方法比 Fang 等人的方法更强大。(2017, JRSSB ) 当预测变量的系数是高维的并且不是很稀疏时。作为一个说明性的例子，我们将我们的程序应用于乳腺癌研究。