Screening for ultrahigh dimensional features may encounter complicated issues such as outlying observations, heteroscedasticity or heavy-tailed distribution, multi-collinearity and confounding effects. Standard correlation-based marginal screening methods may be a weak solution to these issues. We contribute a novel robust joint screener to safeguard against outliers and distribution mis-specification for both the response variable and the covariates, and to account for external variables at the screening step. Specifically, we introduce a copula-based partial correlation (CPC) screener. We show that the empirical process of the estimated CPC converges weakly to a Gaussian process and establish the sure screening property for CPC screener under very mild technical conditions, where we need not require any moment condition, weaker than existing alternatives in the literature. Moreover, our approach allows for a diverging number of conditional variables from the theoretical point of view. Extensive simulation studies and two data applications are included to illustrate our proposal.

中文翻译：

---

基于 Copula 的偏相关筛选：一种联合且稳健的方法

超高维特征的筛选可能会遇到复杂的问题，例如异常观察、异方差或重尾分布、多重共线性和混杂效应。标准的基于相关性的边际筛选方法可能是这些问题的薄弱解决方案。我们提供了一种新颖的强大联合筛选器，以防止响应变量和协变量的异常值和分布错误规范，并在筛选步骤中考虑外部变量。具体来说，我们引入了基于 copula 的偏相关 (CPC) 筛选器。我们表明，估计的 CPC 的经验过程弱收敛到高斯过程，并在非常温和的技术条件下为 CPC 筛选器建立了可靠的筛选特性，我们不需要任何矩条件，比文献中现有的替代方案弱。此外，我们的方法允许从理论角度考虑不同数量的条件变量。包括广泛的模拟研究和两个数据应用程序来说明我们的建议。