  Variable screening has been a useful research area that deals with
ultrahigh-dimensional data. When there exist both marginally and jointly
dependent predictors to the response, existing methods such as conditional
screening or iterative screening often suffer from instability against the
selection of the conditional set or the computational burden, respectively. In
this article, we propose a new independence measure, named conditional
martingale difference divergence (CMDH), that can be treated as either a
conditional or a marginal independence measure. Under regularity conditions, we
show that the sure screening property of CMDH holds for both marginally and
jointly active variables. Based on this measure, we propose a kernel-based
model-free variable screening method, which is efficient, flexible, and stable
against high correlation among predictors and heterogeneity of the response. In
addition, we provide a data-driven method to select the conditional set. In
simulations and real data applications, we demonstrate the superior performance
of the proposed method.
