Risk Bounds For Distributional Regression

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.