  In ultrahigh dimensional setting, independence screening has been both
theoretically and empirically proved a useful variable selection framework with
low computation cost. In this work, we propose a two-step framework by using
marginal information in a different perspective from independence screening. In
particular, we retain significant variables rather than screening out
irrelevant ones. The new method is shown to be model selection consistent in
the ultrahigh dimensional linear regression model. To improve the finite sample
performance, we then introduce a three-step version and characterize its
asymptotic behavior. Simulations and real data analysis show advantages of our
method over independence screening and its iterative variants in certain
regimes.
