论文标题
分布回归及其对CRP的评估：minimax风险的界限和收敛性
Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax risk
论文作者
论文摘要
在过去几十年中，评分规则的属性的理论进步扩大了概率预测中评分规则的使用。在气象预测中，统计后处理技术对于改善确定性物理模型的预测至关重要。许多最先进的统计后处理技术基于与连续排名概率评分（CRP）评估的分布回归。但是，使用CRP的这种评估的理论特性仅考虑了无条件的框架（即没有协变量）和无限样本量。我们扩展了这些结果并研究了分布回归方法的CRP方面的收敛速度。我们发现给定类别的分布的最佳最小收敛速率，并表明k-nearthign方法和内核方法达到了此最佳最小速率。
The theoretical advances on the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to improve the forecasts made by deterministic physical models. Numerous state-of-the-art statistical postprocessing techniques are based on distributional regression evaluated with the Continuous Ranked Probability Score (CRPS). However, theoretical properties of such evaluation with the CRPS have solely considered the unconditional framework (i.e. without covariates) and infinite sample sizes. We extend these results and study the rate of convergence in terms of CRPS of distributional regression methods. We find the optimal minimax rate of convergence for a given class of distributions and show that the k-nearest neighbor method and the kernel method reach this optimal minimax rate.
