Isotonic distributional regression
Isotonic distributional regression
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DOI：
10.1111/rssb.12450
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发表时间：
2019-09
期刊：
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通讯作者：
A. Henzi;J. Ziegel;T. Gneiting
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文献类型：
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作者：
A. Henzi;J. Ziegel;T. Gneiting
保序分布回归(IDR)是在序约束条件下估计条件分布的一种强有力的非参数方法。简而言之，IDR学习条件分布，这些条件分布是经过校准的，并且相对于相关损失函数的综合类同时是最优的，受协变量空间上的偏序的保序约束。非参数保序分位数回归和非参数保序二元回归作为特例出现。对于预测，我们提出了一种在池相邻违规者算法下推广现有规范的内插方法。我们建议在概率预测问题中使用IDR作为一种通用基准技术，因为它不涉及任何参数调整或实现选择，除了在协变量空间上选择偏序。该方法可以与子样本聚合相结合，具有更平滑的回归函数和更高的计算效率。在模拟研究中，我们从连续排序概率分数(CRPS)和L2估计误差这两个密切相关的方面比较了分布回归的方法。在一个来自领先的数值天气预报系统的原始和后处理定量降水预报的案例研究中，IDR与最先进的技术相竞争。
Isotonic distributional regression (IDR) is a powerful non‐parametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and simultaneously optimal relative to comprehensive classes of relevant loss functions, subject to isotonicity constraints in terms of a partial order on the covariate space. Non‐parametric isotonic quantile regression and non‐parametric isotonic binary regression emerge as special cases. For prediction, we propose an interpolation method that generalizes extant specifications under the pool adjacent violators algorithm. We recommend the use of IDR as a generic benchmark technique in probabilistic forecast problems, as it does not involve any parameter tuning nor implementation choices, except for the selection of a partial order on the covariate space. The method can be combined with subsample aggregation, with the benefits of smoother regression functions and gains in computational efficiency. In a simulation study, we compare methods for distributional regression in terms of the continuous ranked probability score (CRPS) and L2 estimation error, which are closely linked. In a case study on raw and post‐processed quantitative precipitation forecasts from a leading numerical weather prediction system, IDR is competitive with state of the art techniques.