# Extremal Quantile Regression: An Overview

arXiv: https://arxiv.org/abs/1612.06850 · HTML: https://mlsanity.com/paper/1612.06850/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2016.

## Built on by (most cited first, 6 of 6)

- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Learning for Spatial Branching: An Algorithm Selection Approach](https://mlsanity.com/paper/2204.10834/) (2022)
- [fastkqr: A Fast Algorithm for Kernel Quantile Regression](https://mlsanity.com/paper/2408.05393/) (2024)
- [Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks](https://mlsanity.com/paper/2505.03034/) (2025)
- [Weighted-average quantile regression](https://mlsanity.com/paper/2203.03032/) (2022)
- [Modelling non-stationary extremal dependence through a geometric approach](https://mlsanity.com/paper/2509.22501/) (2025)

## Abstract (arXiv)

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value approximations to the law of the Koenker and Bassett (1978) quantile regression estimator. Extreme value laws not only have been shown to provide more accurate approximations than Gaussian laws at the tails, but also have served as the basis to develop bias corrected estimators and inference methods using simulation and suitable variations of bootstrap and subsampling. The applicability of these methods is illustrated with two empirical examples on conditional value-at-risk and financial contagion.