Conditional-quantile screening for ultrahigh-dimensional survival data via martingale difference correlation
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Using the so-called martingale difference correlation (MDC), we propose a novel censored-conditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity (which is often present in such data). By incorporating a weighting scheme, this method is a natural extension of MDC-based conditional quantile screening, as considered in Shao and Zhang (2014), to handle ultrahigh-dimensional survival data. The proposed screening procedure has a sure-screening property under certain technical conditions and an excellent capability of detecting the nonlinear relationship between independent and censored dependent variables. Both simulation results and an analysis of real data demonstrate the effectiveness of the new censored conditional quantile-screening procedure.
Keywordsultrahigh-dimensional survival data martingale difference correlation censored-conditional-quantile screening sure-screening property
MSC(2010)62G08 62G20 62H20
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This work was supported by the National Statistical Scientific Research Projects (Grant No. 2015LZ54). The authors thank the two anonymous reviewers for their constructive comments, which have led to a dramatic improvement of the earlier version of this article.