Abstract: Screening for ultrahigh-dimensional features becomes difficult in the presence of outlying observations, heterogeneous or heavy-tailed distributions, multicollinearity, and confounding effects. Standard correlation-based marginal screening methods may offer a weak solution to these problems. We contribute a novel robust joint screener that safeguards against outliers and distribution misspecification of both the response variable and the covariates, and accounts for external variables at the screening step. Specifically, we introduce a copula-based partial correlation (CPC) screener. We show that the empirical process of the estimated CPC converges weakly to a Gaussian process. Furthermore, we establish the sure screening property for the CPC screener under very mild technical conditions, which need not require a moment condition, and are weaker than existing alternatives in the literature. Moreover, from a theoretical perspective, our approach allows for a diverging number of conditional variables. Extensive simulation studies and two data applications demonstrate the effectiveness of the proposed screening method.

Key words and phrases: Copula partial correlation, outlier, sure independent screening.