Low-Rank Regularization of Global Fréchet Regression Models for Distributional Responses

Fréchet regression has emerged as a useful tool for modeling non-Euclidean response variables associated with Euclidean covariates. In this work, we propose a global Fréchet 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.