To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein distance. In the cases where all candidate models are misspecified, we prove that the corresponding model averaging estimator has asymptotic optimality, achieving the lowest possible Wasserstein distance. When there are correctly specified candidate models, we prove that our method asymptotically assigns all weights to the correctly specified models. Numerical results of extensive simulations and a real data analysis on intracerebral hemorrhage data strongly favour our method.

翻译：为应对全局Fréchet回归中的模型不确定性并提升密度响应预测性能，本文提出一种频数模型平均方法。通过最小化基于Wasserstein距离的交叉验证准则确定权重。当所有候选模型均为误设时，我们证明对应的模型平均估计量具有渐近最优性，可实现最低的Wasserstein距离。当存在正确设定的候选模型时，我们证明该方法在渐近意义下将所有权重分配给正确设定的模型。广泛的数值模拟结果及基于脑出血数据的实证分析均显著支持本方法的有效性。