New estimation methods for extremal bivariate return curves

TL;DR

This paper introduces new estimation methods for extremal bivariate return curves using models that capture extremal dependence, validated through simulations and applied to metocean data.

Contribution

It presents novel estimation techniques for bivariate return curves based on extremal value models, with validation tools and uncertainty representation.

Findings

Good performance in simulation studies

Effective application to metocean data

Validation tools for return curve estimates

Abstract

In the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level. Unlike several existing techniques, our estimates are based on bivariate extreme value models that can capture both key forms of extremal dependence. We devise tools for validating return curve estimates, as well as representing their uncertainty, and compare a selection of curve estimation techniques through simulation studies. We apply the methodology to two metocean data sets, with diagnostics indicating generally good performance.