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

ABSTRACT

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.

KEYWORDS:

• Conditional feature screening
• quantile screening
• ranking consistency property
• sure screening property

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62H12
• 62H20

Acknowledgments

We really appreciate that Prof. Yi Li and Dr Hyokyoung G. Hong were able to share with us gene names for the DLBCL data set.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Liu's research was supported by the Fundamental Research Funds for the Central Universities [17CX02035A]. Chen's research was supported by the National Natural Science Foundation of China [11326184, 11501573 and 11771250].