Least Squares Model Averaging Based on Generalized Cross Validation

Frequentist model averaging has received much attention from econometricians and statisticians in recent years. A key problem with frequentist model average estimators is the choice of weights. This paper develops a new approach of choosing weights based on an approximation of generalized cross validation. The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors. Especially, the optimality is built under both discrete and continuous weigh sets. Compared with the existing approach based on Mallows criterion, the conditions required for the asymptotic optimality of the proposed method are more reasonable. Simulation studies and real data application show good performance of the proposed estimators.