Risk Bounds For Distributional Regression
Abstract
This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the worst-case mean squared error (MSE) across the domain. These theoretical results are applied to isotonic and trend filtering distributional regression, yielding convergence rates consistent with those for mean estimation. Furthermore, a general upper bound is derived for distributional regression under non-convex constraints, with a specific application to neural network-based estimators. Comprehensive experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.
Cite
@article{arxiv.2505.09075,
title = {Risk Bounds For Distributional Regression},
author = {Carlos Misael Madrid Padilla and Oscar Hernan Madrid Padilla and Sabyasachi Chatterjee},
journal= {arXiv preprint arXiv:2505.09075},
year = {2025}
}