This article studies model averaging for linear mixed-effects models. We establish an unbiased estimator of the squared risk for the model averaging, and use the estimator as a criterion for choosing weights. The resulting model average estimator is proved to be asymptotically optimal under some regularity conditions. Simulation experiments show it is superior or comparable to estimators based on the final models selected by the commonly-used methods and some existing averaging procedures. The proposed procedure is applied to data from an AIDS clinic trial.

This paper proposes a model averaging method based on Kullback-Leibler distance under a homoscedastic normal error term. The resulting model average estimator is proved to be asymptotically optimal. When combining least squares estimators, the model average estimator is shown to have the same large sample properties as the Mallows model average (MMA) estimator developed by Hansen (2007). We show via simulations that, in terms of mean squared prediction error and mean squared parameter estimation error, the proposed model average estimator is more efficient than the MMA estimator and the estimator based on model selection using the corrected Akaike information criterion in small sample situations. A modified version of the new model average estimator is further suggested for the case of heteroscedastic random errors. The method is applied to a data set from the Hong Kong real estate market.

Functional data is a common and important type in econometrics and has been easier and easier to collect in the big data era. To improve estimation accuracy and reduce forecast risks with functional data, in this paper, we propose a novel cross-validation model averaging method for generalized functional linear model where the scalar response variable is related to a random function predictor by a link function. We establish asymptotic theoretical result on the optimality of the weights selected by our method when the true model is not in the candidate model set. Our simulations show that the proposed method often performs better than the commonly used model selection and averaging methods. We also apply the proposed method to Beijing second-hand house price data.