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Extremal characteristics of conditional models

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>31/03/2023
Issue number1
Number of pages18
Pages (from-to)139-156
Publication StatusPublished
Early online date10/11/22
<mark>Original language</mark>English


Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since the copula and marginals are not expressed in closed forms. We consider bivariate conditional models that specify the distribution of X and the distribution of Y conditional on X. We provide tools to quantify implicit assumptions on the extremes of this class of models. In particular, these tools allow us to approximate the distribution of the tail of Y and the coefficient of asymptotic independence η in closed forms. We apply these methods to a widely used conditional model for wave height and wave period. Moreover, we introduce a new condition on the parameter space for the conditional extremes model of Heffernan and Tawn (Journal of the Royal Statistical Society: Series B (Methodology) 66(3), 497-547, 2004), and prove that the conditional extremes model does not capture η, when η