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.

翻译：为解决预测问题中灵活损失函数下的模型不确定性，我们提出了一种能够适应多种损失函数的模型平均方法，包括非对称线性与二次损失函数，以及作为特例的许多其他非对称/对称损失函数。该灵活损失函数使所提方法能够对大量模型进行平均，例如分位数回归和期望分位数回归模型。为确定候选模型的权重，我们建立了一个J折交叉验证准则。证明了所提方法的渐近最优性及权重收敛性。仿真与实证应用表明，相较于其他模型选择与平均方法，所提方法具有更优的性能。