Conditional quantile correlation learning for ultrahigh dimensional varying coefficient models and its application in survival analysis
Conditional quantile correlation learning for ultrahigh dimensional varying coefficient models and its application in survival analysis
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DOI：
10.5705/ss.202016.0402
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发表时间：
2018
影响因子：
1.4
通讯作者：
Xiaochao Xia;Jialiang Li;B. Fu
中科院分区：
文献类型：
--
作者：
Xiaochao Xia;Jialiang Li;B. Fu
本文考虑变系数模型下超高维变量筛选的一种稳健方法。针对已有工作主要关注均值回归函数的情况，提出了一种基于条件分位数相关性确定独立性筛选(CQCSIS)的方法。该方法一般适用于异质或重尾数据，对响应的单调变换不变。此外，我们将这种筛选过程推广到通过逆概率加权来处理截尾寿命数据。由于应用了非参数B-样条法，CQCSIS可以很容易地实现，并且计算速度比基于核的筛选方法快得多。在一定的正则性条件下，我们对所提出的方法建立了确定的筛选性质，包括筛选一致性和排序一致性。为了进一步提高CQCSIS的性能，我们还尝试构建了一个基于群SCAD惩罚的两阶段变量选择过程。文中还给出了大量的仿真实例和数据应用。
In this paper, we consider a robust approach to the ultrahigh dimensional variable screening under varying coefficient models. While the existing works focusing on the mean regression function, we propose a procedure based on conditional quantile correlation sure independence screening (CQCSIS). This proposal is applicable to heterogeneous or heavy-tailed data in general and is invariant to monotone transformation of the response. Furthermore, we generalize such a screening procedure to address censored lifetime data through inverse probability weighting. The CQCSIS can be easily implemented, due to an application of nonparametric B-spline approximation, and computed much faster than the kernel based screening method. Under some regularity conditions, we establish sure screening properties including screening consistency and ranking consistency for proposed approaches. We also attempt to construct a two-stage variable selection procedure for a further improvement of performance of CQCSIS based on a group SCAD penalization. Extensive simulation examples and data applications are presented for illustration.