Minimum Mean Squared Error Model Averaging in Likelihood Models

Abstract

A data-driven method for frequentist model averaging weight choice is developed for general likelihood models. We propose to estimate the weights which minimize an estimator of the mean squared error of a weighted estimator in a local misspecification framework. We find that in general there is not a unique set of such weights, meaning that predictions from multiple model averaging estimators will not be identical. This holds in both the univariate and multivariate case. However, we show that a unique set of empirical weights is obtained if the candidate models are appropriately restricted. In particular a suitable class of models are the so-called singleton models where each model only includes one parameter from the candidate set. This restriction results in a drastic reduction in the computational cost of model averaging weight selection relative to methods which include weights for all possible parameter subsets. We investigate the performance of our methods in both linear models and generalized linear models, and illustrate the methods in two empirical applications.

Keywords: Frequentist model averaging, mean squared error, weight choice, local misspecification, likelihood regression