  Model selection strategies have been routinely employed to determine a model
for data analysis in statistics, and further study and inference then often
proceed as though the selected model were the true model that were known a
priori. This practice does not account for the uncertainty introduced by the
selection process and the fact that the selected model can possibly be a wrong
one. Model averaging approaches try to remedy this issue by combining
estimators for a set of candidate models. Specifically, instead of deciding
which model is the 'right' one, a model averaging approach suggests to fit a
set of candidate models and average over the estimators using certain data
adaptive weights. In this paper we establish a general frequentist model
averaging framework that does not set any restrictions on the set of candidate
models. It greatly broadens the scope of the existing methodologies under the
frequentist model averaging development. Assuming the data is from an unknown
model, we derive the model averaging estimator and study its limiting
distributions and related predictions while taking possible modeling biases
into account. We propose a set of optimal weights to combine the individual
estimators so that the expected mean squared error of the average estimator is
minimized. Simulation studies are conducted to compare the performance of the
estimator with that of the existing methods. The results show the benefits of
the proposed approach over traditional model selection approaches as well as
existing model averaging methods.

Methodology