# Automated threshold selection and associated inference uncertainty for univariate extremes

arXiv: https://arxiv.org/abs/2310.17999 · HTML: https://mlsanity.com/paper/2310.17999/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2023.

## Built on by (most cited first, 3 of 3)

- [GPDFlow: Generative Multivariate Threshold Exceedance Modeling via Normalizing Flows](https://mlsanity.com/paper/2503.11822/) (2025)
- [Modelling non-stationary extremal dependence through a geometric approach](https://mlsanity.com/paper/2509.22501/) (2025)
- [Stop Suppressing the Tail: Causal Inference for Extreme Events](https://mlsanity.com/paper/2605.27474/) (2026)

## Abstract (arXiv)

Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples is difficult and highly subjective through standard methods. Inference for high quantiles can also be highly sensitive to the choice of threshold. Too low a threshold choice leads to bias in the fit of the extreme value model, while too high a choice leads to unnecessary additional uncertainty in the estimation of model parameters. We develop a novel methodology for automated threshold selection that directly tackles this bias-variance trade-off. We also develop a method to account for the uncertainty in the threshold estimation and propagate this uncertainty through to high quantile inference. Through a simulation study, we demonstrate the effectiveness of our method for threshold selection and subsequent extreme quantile estimation, relative to the leading existing methods, and show how the method's effectiveness is not sensitive to the tuning parameters. We apply our method to the well-known, troublesome example of the River Nidd dataset.