  We introduce a computationally effective algorithm for a linear model
selection consisting of three steps: screening--ordering--selection (SOS).
Screening of predictors is based on the thresholded Lasso that is l_1 penalized
least squares. The screened predictors are then fitted using least squares (LS)
and ordered with respect to their t statistics. Finally, a model is selected
using greedy generalized information criterion (GIC) that is l_0 penalized LS
in a nested family induced by the ordering. We give non-asymptotic upper bounds
on error probability of each step of the SOS algorithm in terms of both
penalties. Then we obtain selection consistency for different (n, p) scenarios
under conditions which are needed for screening consistency of the Lasso. For
the traditional setting (n >p) we give Sanov-type bounds on the error
probabilities of the ordering--selection algorithm. Its surprising consequence
is that the selection error of greedy GIC is asymptotically not larger than of
exhaustive GIC. We also obtain new bounds on prediction and estimation errors
for the Lasso which are proved in parallel for the algorithm used in practice
and its formal version.
