Optimal model averaging for multivariate regression models

In this paper, frequentist model averaging is considered in the context of a multivariate multiple regression model. We propose a weight choice criterion based on a plug-in counterpart of the quadratic risk of the model average estimator that involves an approximation of the distribution of a ratio of quadratic forms by an F distribution. We establish an asymptotic theory for the resultant model average estimator for both the general and restricted weight sets, and derive the convergence rate of the model weights to the quadratic risk-based optimal weights. The merits of our approach are illustrated by a simulation study and an application based on from the Sixth National Population Census of China.