Conditional quantile correlation learning for ultrahigh dimensional varying coefficient models and its application in survival analysis

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.

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