# Estimation and uncertainty quantification for extreme quantile regions

arXiv: https://arxiv.org/abs/1904.08251 · HTML: https://mlsanity.com/paper/1904.08251/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Extreme Risk Mitigation in Reinforcement Learning using Extreme Value Theory](https://mlsanity.com/paper/2308.13011/) (2023)
- [EX-DRL: Hedging Against Heavy Losses with EXtreme Distributional Reinforcement Learning](https://mlsanity.com/paper/2408.12446/) (2024)

## Abstract (arXiv)

Estimation of extreme quantile regions, spaces in which future extreme events can occur with a given low probability, even beyond the range of the observed data, is an important task in the analysis of extremes. Existing methods to estimate such regions are available, but do not provide any measures of estimation uncertainty. We develop univariate and bivariate schemes for estimating extreme quantile regions under the Bayesian paradigm that outperforms existing approaches and provides natural measures of quantile region estimate uncertainty. We examine the method's performance in controlled simulation studies. We illustrate the applicability of the proposed method by analysing high bivariate quantiles for pairs of pollutants, conditionally on different temperature gradations, recorded in Milan, Italy.