Isotonic distributional regression

• 成果类型: Article
• 署名作者: Henzi, Alexander; Ziegel, Johanna F.; Gneiting, Tilmann
• 署名单位: University of Bern; Heidelberg Institute for Theoretical Studies; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12450
• 发表日期: 2021
• 页码: 963-993
• 关键词: probabilistic forecasts; Scoring rules; ensemble; prediction; quantile; ambiguity; models; rainfall; forests; ecmwf

摘要

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.