Fitting sparse linear models under the sufficient and necessary condition for model identification

Abstract We propose an enhanced support detection and root finding approach (ESDAR) to variable selection in sparse linear models. ESDAR is motivated from the KKT conditions for the l 0 penalized regression. In ESDAR, we introduce a step size to balance the primal and dual variables in determining the support of the solution. We establish a sharp oracle error bound and an oracle support recovery property for the solution sequence generated by ESDAR under the weakest possible condition on the design matrix that is sufficient and necessary for the model to be identifiable. The conditions for the oracle results we obtained are weaker than those for Lasso and concave selection methods including SCAD and MCP in the literature.