为分布回归提供理论风险上界，验证了多种方法的收敛性。
Risk Bounds For Distributional Regression
- 基于凸约束建立CRPS与最大均方误差上界
- 在等序与趋势滤波中获得与均值估计一致的收敛速度
- 扩展至非凸约束，适用于神经网络估计器
本文研究非参数分布回归估计器的风险上界。针对凸约束下的分布回归，建立了连续分级概率评分（CRPS）和全域最差情况均方误差（MSE）的一般上界。这些理论结果被应用于等序与趋势滤波分布回归，得到了与均值估计一致的收敛速率。此外，还推导了非凸约束下分布回归的一般上界，并具体应用于基于神经网络的估计器。在模拟数据和真实数据上的全面实验验证了理论贡献，展示了其实际有效性。
原文摘要 · Abstract (English)
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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