Frequentist Model Averaging for Global Fr\'{e}chet Regression

TL;DR

This paper introduces a frequentist model averaging approach for global Fréchet regression that optimally combines models to improve density prediction, especially under model misspecification, using Wasserstein distance.

Contribution

It proposes a novel model averaging method with weight selection via cross-validation, ensuring asymptotic optimality and correct model identification in Fréchet regression.

Findings

Method achieves asymptotic optimality under misspecification

Correctly specified models receive all weights asymptotically

Numerical experiments and real data analysis validate effectiveness

Abstract

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.