Model Selection in Large Dimensional Linear Regression using Sequential Multiple Testing

High dimensional regression specification and analysis is a complex and active area of research in statistics and econometrics. A large number of approaches has been proposed each with its own limitations and challenges. This paper proposes a new hybrid approach combining elements from two existing methods. The first is the greedy methodology developed by Chudik et al. (2018), where a powerful multiple testing step introduces parsimony, by ensuring that completely irrelevant variables are not selected, with high probability. The second is stage-wise regression where relevant variables are selected in steps, rather than jointly as in Chudik et al. (2018). However, in that literature the stopping rules, which typically rely on model information criteria, are not sufficiently parsimonious. We derive some theoretical properties of the new method and show, through simulations, that it performs well. An illustration, using corporate emissions data, provides an empirical perspective.