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.
翻译:在过去几十年里,在评分规则特性方面的理论进步扩大了在概率预测中使用评分规则的范围;在气象预报中,统计后处理技术对于改进确定物理模型的预测至关重要;许多最先进的统计后处理技术是以连续排位概率分数评估的分布回归为基础的;然而,与CRPS进行的这种评价的理论特性仅考虑了无条件框架(即无共变)和无限样本大小;我们推广了这些结果,并研究了分配回归法的CRPS趋同率;我们找到了某一类分配的最佳微缩趋同率,并表明K-最早期的邻里方法和内核法达到了这一最佳微缩轴速率。