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. Copyright 2003 Blackwell Publishing Ltd.