In this paper, we innovatively propose an extremely flexible semi-parametric regression model called Multi-response Trans-Elliptical Regression (MTER) Model, which can capture the heavy-tail characteristic and tail dependence of both responses and covariates. We investigate the feature screening procedure for the MTER model, in which Kendall’ tau-based canonical correlation estimators are proposed to characterize the correlation between each transformed predictor and the multivariate transformed responses. The main idea is to substitute the classical canonical correlation ranking index in [X. B. Kong, Z. Liu, Y. Yao and W. Zhou, Sure screening by ranking the canonical correlations, TEST 26 (2017) 1–25] by a carefully constructed non-parametric version. The sure screening property and ranking consistency property are established for the proposed procedure. Simulation results show that the proposed method is much more powerful to distinguish the informative features from the unimportant ones than some state-of-the-art competitors, especially for heavy-tailed distributions and high-dimensional response. At last, a real data example is given to illustrate the effectiveness of the proposed procedure.

中文翻译：

---

具有超高维协变量的多响应反椭圆回归模型的稳健特征筛选

在本文中，我们创新性地提出了一种极其灵活的半参数回归模型，称为多响应跨椭圆回归 (MTER) 模型，该模型可以捕捉响应和协变量的重尾特征和尾依赖关系。我们研究了 MTER 模型的特征筛选程序，其中提出了基于 Kendall tau 的典型相关估计器来表征每个变换预测变量与多变量变换响应之间的相关性。主要思想是用精心构造的方法代替 [XB Kong, Z. Liu, Y. Yao and W. Zhou, Sure screenshot by rating the canonical correlation, TEST 26 (2017) 1-25] 中的经典典型相关排名指数非参数版本。为所提出的程序建立了确定筛选属性和排序一致性属性。仿真结果表明，所提出的方法在区分信息特征和不重要特征方面比一些最先进的竞争对手更强大，特别是对于重尾分布和高维响应。最后，给出了一个真实的数据例子来说明所提出程序的有效性。