Isotonic Distributional Regression
Speaker: Richard Zhu
Abstract: Isotonic distributional regression (IDR) is a nonparametric technique for the estimation of conditional distributions under order restrictions within the covariate space. It is a natural generalization of estimating single-valued functional such as isotonic regression/isotonic quantile regression. I will start with defining IDR in terms of its uniqueness and optimality with respect to the continuous ranked probability score (CRPS). Then I will talk about its universality in the sense that it is also optimal with respect to a broader class of proper scoring rules. Finally, I will discuss its uniform consistency if time permits. The results are mainly based on the following papers: [1] https://arxiv.org/abs/1909.03725 and [2] https://link.springer.com/article/10.1007/s10463-021-00808-0