Isotonic Distributional Regression

Abstract Isotonic distributional regression (IDR) is a powerful non-parametric technique for the estimation of conditional distributions under order restrictions. In nutshell, IDR learns that are calibrated, and simultaneously optimal relative to comprehensive classes relevant loss functions, subject isotonicity constraints in terms partial on covariate space. Non-parametric isotonic quantile binary emerge as special cases. For prediction, we propose an interpolation method generalizes extant specifications pool adjacent violators algorithm. We recommend use generic benchmark probabilistic forecast problems, it does not involve any parameter tuning nor implementation choices, except selection The can be combined with subsample aggregation, benefits smoother functions gains computational efficiency. simulation study, compare methods continuous ranked probability score (CRPS) L2 error, which closely linked. case study raw post-processed quantitative precipitation forecasts from leading numerical weather prediction system, competitive state art techniques.