  In this article, we propose a novel variable screening method for linear
models named as conditional screening via ordinary least squares projection
(COLP). COLP can take advantage of prior knowledge concerning certain active
predictors by eliminating the adverse impact of their coefficients in the
estimation of remaining ones and thus significantly enhance the screening
accuracy. We prove its sure-screening property under reasonable assumptions and
demonstrate its utility in an application to a leukemia dataset. Moreover,
based on the conditional approach, we introduce an iterative algorithm named as
forward screening via ordinary least squares projection (FOLP), which not only
could exploit the prior information more effectively, but also has promising
performance when no prior knowledge is available using a data-driven
conditioning set. Extensive simulation studies are carried out to demonstrate
the competence of both proposed methods.
