A strongly consistent procedure for model selection in a regression problem

We consider the multiple regression model Yn= Xnβ+ En, where Yn and En are n-vector random variables, Xn is an n×m matrix and β is an m-vector of unknown regression parameters. Each component of β may be zero or nonzero, which gives rise to 2m possible models for multiple regression. We provide a decision rule for the choice of a model which is strongly consistent for the true model as n →∞. The result is proved under certain mild conditions, for instance without assuming normality of the distribution of the components of En.