New estimation methods for extremal bivariate return curves

Murphy-Barltrop, Callum and Wadsworth, Jennifer and Eastoe, Emma (2023) New estimation methods for extremal bivariate return curves. Environmetrics, 34 (5): e2797. ISSN 1180-4009

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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 met-ocean data sets, with diagnostics indicating generally good performance.