On the least-squares model averaging interval estimator

In many applications of linear regression models, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty, least-squares frequentist model averaging has been proposed recently. We show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. The finite-sample confidence intervals based on approximations to the asymptotic distributions are also equivalent if the parameter of interest is a linear function of the regression coefficients. Furthermore, we demonstrate that this equivalence also holds for prediction intervals constructed in the same fashion.