  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.

Methodology