Quantile screening for ultra-high-dimensional heterogeneous data conditional on some variables

In this paper, we propose a conditional quantile independence screening approach for ultra-high-dimensional heterogeneous data given some known, significant and low-dimensional variables. The new method does not require imposing a specific model structure for the response and covariates and can detect additional features that contribute to conditional quantiles of the response given those already-identified important predictors. We also prove that the proposed procedure enjoys the ranking consistency and sure screening properties. Some simulation studies are carried out to examine the performance of advised procedure. At last, we illustrate it by a real data example.