Frequentist model averaging for envelope models

The envelope method produces efficient estimation in multivariate linear regression, and is widely applied in biology, psychology, and economics. This paper estimates parameters through a model averaging methodology and promotes the predicting abilities of the envelope models. We propose a frequentist model averaging method by minimizing a cross-validation criterion. When all the candidate models are misspecified, the proposed model averaging estimator is proved to be asymptotically optimal. When correct candidate models exist, the coefficient estimator is proved to be consistent, and the sum of the weights assigned to the correct models, in probability, converges to one. Simulations and an empirical application demonstrate the effectiveness of the proposed method.