CONSISTENT VARIABLE SELECTION IN LINEAR-MODELS

A method of estimating linear model dimension and variable selection i s proposed. This new criterion, which generalizes the C-p criterion, t he Akaike information criterion (AIC), the Bayes information criterion , and the phi criterion and is consistent under certain conditions, is based on a new class of penalty functions and a procedure of sorting covariates based on t-statistics. In the course of introducing this me thod, we discuss the important role of the penalty function in the con sistency of model dimension estimation and in variable selection. The proposed method requires less computation than resampling-based method s that search over all subsets of covariates for the true model. Simul ation results show that the new method is superior to the C-p criterio n and AIC in finite-sample situations as well.