To address model uncertainty under flexible loss functions in prediction p blems, 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 weight 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：针对预测问题中灵活损失函数下的模型不确定性，本文提出一种能够适应多种损失函数的模型平均方法，该方法涵盖非对称线性与二次损失函数，并将诸多其他非对称/对称损失函数作为特例纳入统一框架。该灵活损失函数使得所提方法能够对分位数回归和期望分位数回归等广泛模型进行加权平均。为确定候选模型的权重，我们建立了J折交叉验证准则。从理论上证明了所提方法的渐近最优性及权重收敛性。仿真实验与实证应用表明，相较于其他模型选择与平均方法，所提方法具有更优越的性能。