Isotonic regression for functionals of elicitation complexity greater than one

TL;DR

This paper investigates isotonic regression for bivariate elicitable functionals, such as mean-variance and Value-at-Risk with Expected Shortfall, focusing on ordered covariates and extending to partial orders.

Contribution

It introduces non-parametric isotonic regression methods for complex elicitable functionals and extends results to partial orders.

Findings

Addresses isotonic regression for bivariate elicitable functionals.

Provides extensions to partial order covariates.

Focuses on risk measures like Value-at-Risk and Expected Shortfall.

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.