# Frequentist Model Averaging for Global Fr'echet Regression

arXiv: https://arxiv.org/abs/2309.01691 · HTML: https://mlsanity.com/paper/2309.01691/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses](https://mlsanity.com/paper/2510.17072/) (2025)
- [Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Age](https://mlsanity.com/paper/2501.06868/) (2025)
- [Dynamic Frechet Regression with Feature Selection for Distributional Data](https://mlsanity.com/paper/2607.09613/) (2026)

## Abstract (arXiv)

To consider model uncertainty in global Fr'echet 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.