Consistency of model averaging estimators

•The local mis-specification is not assumed in this paper.•I prove the root-n consistency of Smoothed AIC and Smoothed BIC estimators.•I prove the root-n consistency of Mallows model averaging and jackknife model averaging estimators.

Recently, there has been increasing interest in model averaging within frequentist paradigm. In the existing literature, for proving consistency of model averaging estimators, local mis-specification is assumed. In this paper, we show that under general fixed parameter setup, the model averaging estimators remain root-n consistent. This result provides a new theoretical basis for the use of model averaging estimators.