Low-Rank Regularization of Global Fr\'{e}chet Regression Models for Distributional Responses

TL;DR

This paper introduces a low-rank regularized global Fréchet regression method for distributional responses, improving efficiency and accuracy in modeling non-Euclidean data with theoretical guarantees and numerical validation.

Contribution

It proposes a novel low-rank regularization approach for global Fréchet regression models with distributional responses, enhancing robustness and estimation accuracy.

Findings

Low-rank regularization improves model efficiency.

The method outperforms standard techniques in finite-sample tests.

Theoretical analysis confirms robustness and consistency.

Abstract

Fr\'echet regression has emerged as a useful tool for modeling non-Euclidean response variables associated with Euclidean covariates. In this work, we propose a global Fr\'echet regression estimation method that incorporates low-rank regularization. Focusing on distribution function responses, we demonstrate that leveraging the low-rank structure of the model parameters enhances both the efficiency and accuracy of model fitting. Through theoretical analysis of the large-sample properties, we show that the proposed method enables more robust modeling and estimation than standard dimension reduction techniques. To support our findings, we also present numerical experiments that evaluate the finite-sample performance.