Risk Bounds For Distributional Regression

• URL: http://arxiv.org/abs/2505.09075v3
• Date: Fri, 11 Jul 2025 22:57:43 GMT
• Title: Risk Bounds For Distributional Regression
• Authors: Carlos Misael Madrid Padilla, Oscar Hernan Madrid Padilla, Sabyasachi Chatterjee,
• Abstract summary: General upper bounds are established for the continuous ranked score (CRPS) and the worst-case mean squared error (MSE) across the domain.<n>Experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.
• Score: 9.92024586772767
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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