Limit of the optimal weight in least squares model averaging with non-nested models

Recently, there has been increasing interest in the asymptotic limits of the optimal weight and the model averaging estimator within frequentist paradigm. Most existing literatures assume the candidate models are nested in such studies and the extension to non-nested models are not trivial. In the paper, we derive the asymptotic limit of the optimal weight in least squares model averaging when the candidate models are non-nested and could be all under-fitted. This result provides more insights into least squares model averaging and a new technique for future studies.