To consider model uncertainty in global Fréchet 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.

Publication:

IEEE Transactions on Information Theory ( Volume: 71, Issue: 3, March 2025)

http://dx.doi.org/10.1109/TIT.2024.3520979

Author:

Xingyu Yan

the School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China, and also with the International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

e-mail: yan@jsnu.edu.cn

Xinyu Zhang

the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

e-mail: xinyu@amss.ac.cn

Peng Zhao

the School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

e-mail: zhaop@jsnu.edu.cn