Isotonic distributional regression
Isotonic distributional regression (IDR) is a nonparametric distributional regression approach under a monotonicity constraint. It has found application as a generic method for uncertainty quantification, in statistical postprocessing of weather forecasts, and it is an integral part of distributional single index models. IDR has favorable calibration and optimality properties in finite samples.
Furthermore, it has an interesting population counterpart called isotonic conditional laws that generalize conditional distributions with respect to σ-algebras to conditional distributions with respect to σ-lattices. In this talk, an overview of the theory and some applications of IDR are presented.