Model Averaging Under Flexible Loss Functions

Abstract: To address model uncertainty under flexible loss functions in prediction problems, we propose a model averaging method that accommodates various loss functions, including asymmetric linear and quadratic loss functions, as well as many other asymmetric/symmetric loss functions as special cases. The flexible loss function allows the proposed method to average a large range of models, such as the quantile and expectile regression models. To determine the weights of the candidate models, we establish a J-fold cross-validation criterion. Asymptotic optimality and weights convergence are proved for the proposed method. Simulations and an empirical application show the superior performance of the proposed method, compared with other methods of model selection and averaging.