# Threshold Selection in Univariate Extreme Value Analysis

## TL;DR

This paper introduces two new automated, parameter-free methods for threshold selection in univariate extreme value analysis, improving the estimation of rare event quantiles and adapting to changing data characteristics.

## Contribution

The paper presents two novel threshold selection procedures that do not require manual tuning, enhancing the automation and robustness of extreme value analysis.

## Key findings

- Both methods outperform existing procedures in simulations.
- The methods provide reliable estimates across diverse distributions.
- Application to financial data demonstrates practical utility.

## Abstract

Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be chosen by the practitioner. To simplify the use of automated, data-driven threshold selection methods, we introduce two new procedures not requiring the manual choice of any parameters. The first method measures the deviation of the log-spacings from the exponential distribution and achieves good performance in simulations for estimating high quantiles. The second approach smoothly estimates the asymptotic mean square error of the Hill estimator and performs consistently well over a wide range of distributions. The methods are compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time. This application strongly emphasizes the importance of solid automated threshold selection.