  Screening for ultrahigh dimensional features may encounter complicated issues
such as outlying observations, heteroscedasticity or heavy-tailed distribution,
multi-collinearity and confounding effects. Standard correlation-based marginal
screening methods may be a weak solution to these issues. We contribute a novel
robust joint screener to safeguard against outliers and distribution
mis-specification for both the response variable and the covariates, and to
account 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
and establish the sure screening property for CPC screener under very mild
technical conditions, where we need not require any moment condition, weaker
than existing alternatives in the literature. Moreover, our approach allows for
a diverging number of conditional variables from the theoretical point of view.
Extensive simulation studies and two data applications are included to
illustrate our proposal.
