Abstract
We study the non-parametric isotonic regression problem for bivariate elicitable functionals that are given as an elicitable univariate functional and its Bayes risk. Prominent examples for functionals of this type are (mean, variance) and (Value-at-Risk, Expected Shortfall), where the latter pair consists of important risk measures in finance. We present our results for totally ordered covariates but extenstions to partial orders are given in the appendix.
Funding Statement
The authors gratefully acknowledge funding from the Swiss National Science Foundation.
Acknowledgments
The authors are grateful for constructive comments of two anonymous reviewers, which improved the paper.
Citation
Anja Mühlemann. Johanna Ziegel. "Isotonic regression for elicitable functionals and their Bayes risk." Electron. J. Statist. 16 (2) 3836 - 3860, 2022. https://doi.org/10.1214/22-EJS2034
