  Feature screening for ultrahigh-dimension, in general, proceeds with two
essential steps. The first step is measuring and ranking the marginal
dependence between response and covariates, and the second is determining the
threshold. We develop a new screening procedure, called SIT-BY procedure, that
possesses appealing statistical properties in both steps. By employing sliced
independence estimates in the measuring and ranking stage, our proposed
procedure requires no model assumptions, remains invariant to monotone
transformation, and achieves almost linear computation complexity. Inspired by
false discovery rate (FDR) control procedures, we offer a data-adaptive
threshold benefit from the asymptotic normality of test statistics. Under
moderate conditions, we demonstrate that our procedure can asymptotically
control the FDR while maintaining the sure screening property. We investigate
the finite sample performance of our proposed procedure via extensive
simulations and an application to genome-wide dataset.
