Optimal model averaging estimator for expectile regressions

In this paper, we consider model averaging for expectile regressions, which are common in many fields. The J -fold cross-validation criterion is developed to determine averaging weights. Under some regularity conditions, we prove that the resulting model averaging estimators are asymptotically optimal in the sense that they produce an expectile loss that is asymptotically equivalent to that of an infeasible best-possible model averaging estimator. When the true model is one of the candidate models, the averaged estimators are consistent. Simulation experiments suggest that the proposed method is superior to other competing model selection and averaging methods. Finally, empirical applications on excess stock returns and wages illustrate the proposed method.