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Isotonic distributional regression

Henzi, Alexander; Ziegel, Johanna F.; Gneiting, Tilmann 1
1 Karlsruher Institut für Technologie (KIT)


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. ... mehr

Verlagsausgabe §
DOI: 10.5445/IR/1000138357
Veröffentlicht am 30.09.2021
DOI: 10.1111/rssb.12450
Zitationen: 7
Web of Science
Zitationen: 7
Zitationen: 19
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 11.2021
Sprache Englisch
Identifikator ISSN: 1369-7412, 1467-9868
KITopen-ID: 1000138357
Erschienen in Journal of the Royal Statistical Society / B
Verlag John Wiley and Sons
Band 83
Heft 5
Seiten 963-993
Vorab online veröffentlicht am 26.08.2021
Nachgewiesen in Web of Science
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