  Two popular variable screening methods under the ultra-high dimensional
setting with the desirable sure screening property are the sure independence
screening (SIS) and the forward regression (FR). Both are classical variable
screening methods and recently have attracted greater attention under the new
light of high-dimensional data analysis. We consider a new and simple screening
method that incorporates multiple predictors in each step of forward
regression, with decision on which variables to incorporate based on the same
criterion. If only one step is carried out, it actually reduces to the SIS.
Thus it can be regarded as a generalization and unification of the FR and the
SIS. More importantly, it preserves the sure screening property and has similar
computational complexity as FR in each step, yet it can discover the relevant
covariates in fewer steps. Thus, it reduces the computational burden of FR
drastically while retaining advantages of the latter over SIS. Furthermore, we
show that it can find all the true variables if the number of steps taken is
the same as the correct model size, even when using the original FR. An
extensive simulation study and application to two real data examples
demonstrate excellent performance of the proposed method.
