Consistent model selection by an automatic Gets approach

We establish the consistency of the selection procedures embodied in PcGets, and compare their performance with other model selection criteria in linear regressions. The significance levels embedded in the PcGets Liberal and Conservative algorithms coincide in very large samples with those implicit in the Hannan-Quinn (HQ) and Schwarz information criteria (SIC), respectively. Thus, both PcGets rules are consistent under the same conditions as HQ and SIC. However, PcGets has a rather different finite-sample behaviour. Pre-selecting to remove many of the candidate variables is confirmed as enhancing the performance of SIC.