Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations

In this article, we propose a new conditional quantile correlation and establish its connection with conditional quantile regression coefficient functions. We further introduce a conditional quantile screening method based on this metric for varying coefficient models with ultrahigh dimensional features. Under some technical conditions, the proposed approach is shown to enjoy desirable theoretical properties, including ranking consistency and sure screening properties. The extent of the new method's dimensionality reduction is also qualified. To reduce the false selection rate, an iterative algorithm is proposed for improving the accuracy of variable screening. We conduct simulation studies to demonstrate that the proposed screening method can perform reasonably well, and we illustrate the proposed methodology through a real data analysis.