  As a computationally fast and working efficient tool, sure independence
screening has received much attention in solving ultrahigh dimensional
problems. This paper contributes two robust sure screening approaches that
simultaneously take into account heteroscedasticity, outliers, heavy-tailed
distribution, continuous or discrete response, and confounding effect, from the
perspective of model-free. First, we define a robust correlation measure only
using two random indicators, and introduce a screener using that correlation.
Second, we propose a robust partial correlation-based screening approach when
an exposure variable is available. To remove the confounding effect of the
exposure on both response and each covariate, we use a nonparametric regression
with some specified loss function. More specifically, a robust
correlation-based screening method (RC-SIS) and a robust partial
correlation-based screening framework (RPC-SIS) including two concrete
screeners: RPC-SIS(L2) and RPC-SIS(L1), are formed. Third, we establish sure
screening properties of RC-SIS for which the response variable can be either
continuous or discrete, as well as those of RPC-SIS(L2) and RPC-SIS(L1) under
some regularity conditions. Our approaches are essentially nonparametric, and
perform robustly for both the response and the covariates. Finally, extensive
simulation studies and two applications are carried out to demonstrate the
superiority of our proposed approaches.
