Variable selection is a challenging issue in statistical applications when
the number of predictors $p$ far exceeds the number of observations $n$. In
this ultra-high dimensional setting, the sure independence screening (SIS)
procedure was introduced to significantly reduce the dimensionality by
preserving the true model with overwhelming probability, before a refined
second stage analysis. However, the aforementioned sure screening property
strongly relies on the assumption that the important variables in the model
have large marginal correlations with the response, which rarely holds in
reality. To overcome this, we propose a novel and simple screening technique
called the high-dimensional ordinary least-squares projection (HOLP). We show
that HOLP possesses the sure screening property and gives consistent variable
selection without the strong correlation assumption, and has a low
computational complexity. A ridge type HOLP procedure is also discussed.
Simulation study shows that HOLP performs competitively compared to many other
marginal correlation based methods. An application to a mammalian eye disease
data illustrates the attractiveness of HOLP.