  Feature screening approaches are effective in selecting active features from
data with ultrahigh dimensionality and increasing complexity; however, the
majority of existing feature screening approaches are either restricted to a
univariate response or rely on some distribution or model assumptions. In this
article, we propose a novel sure independence screening approach based on the
multivariate rank distance correlation (MrDc-SIS). The MrDc-SIS achieves
multiple desirable properties such as being distribution-free, completely
nonparametric, scale-free, robust for outliers or heavy tails, and sensitive
for hidden structures. Moreover, the MrDc-SIS can be used to screen either
univariate or multivariate responses and either one dimensional or
multi-dimensional predictors. We establish the asymptotic sure screening
consistency property of the MrDc-SIS under a mild condition by lifting previous
assumptions about the finite moments. Simulation studies demonstrate that
MrDc-SIS outperforms three other closely relevant approaches under various
settings. We also apply the MrDc-SIS approach to a multi-omics ovarian
carcinoma data downloaded from The Cancer Genome Atlas (TCGA).
