# Estimation of Spectral Risk Measures

arXiv: https://arxiv.org/abs/1912.10398 · HTML: https://mlsanity.com/paper/1912.10398/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2019.

## Built on by (most cited first, 9 of 9)

- [Spectral risk-based learning using unbounded losses](https://mlsanity.com/paper/2105.04816/) (2021)
- [A Survey of Risk-Aware Multi-Armed Bandits](https://mlsanity.com/paper/2205.05843/) (2022)
- [Stochastic Optimization for Spectral Risk Measures](https://mlsanity.com/paper/2212.05149/) (2022)
- [Online Estimation and Optimization of Utility-Based Shortfall Risk](https://mlsanity.com/paper/2111.08805/) (2021)
- [A Survey of Learning Criteria Going Beyond the Usual Risk](https://mlsanity.com/paper/2110.04996/) (2021)
- [Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivity](https://mlsanity.com/paper/2208.03066/) (2022)
- [A Distribution Optimization Framework for Confidence Bounds of Risk Measures](https://mlsanity.com/paper/2306.07059/) (2023)
- [Concentration Bounds for Optimized Certainty Equivalent Risk Estimation](https://mlsanity.com/paper/2405.20933/) (2024)
- [Risk-aware linear bandits with convex loss](https://mlsanity.com/paper/2209.07154/) (2022)

## Abstract (arXiv)

We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the case when the underlying distribution is either Gaussian or exponential, and derive a concentration bound for our estimation scheme. We validate the theoretical findings on a synthetic setup, and in a vehicular traffic routing application.