On the equivalence of confidence interval estimation based on frequentist model averagingand least-squares for the full model in linear regression

In many applications of linear regression models, model selection is vital. However, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty in these linear models, least squares frequentist model averaging has been proposed recently. In this paper, we show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. Furthermore, we demonstrate that this equivalence also holds in finite samples if the parameter of interest is a linear function of the regression coefficients