A different approach for choosing a threshold in peaks over threshold

TL;DR

This paper introduces a Bayesian method for selecting optimal thresholds in peaks over threshold analysis, improving the accuracy and objectivity of extreme value modeling.

Contribution

It develops a generalized model with a Bayesian approach to determine thresholds without relying on visual inspection, enhancing extreme value analysis.

Findings

Posterior distribution aids in threshold selection.

Method reduces bias and variance in extreme value estimates.

Applicable to gamma positive domain data.

Abstract

Abstract In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but choosing the threshold too high results in uncontrolled variances. This paper investigates a generalized model that can assist in the choice of optimal threshold values in the \gamma positive domain. A Bayesian approach is considered by deriving a posterior distribution for the unknown generalized parameter. Using the properties of the posterior distribution allows for a method to choose an optimal threshold without visual inspection.