Extremal characteristics of conditional models

Tendijck, Stan and Tawn, Jonathan and Jonathan, Philip (2022) Extremal characteristics of conditional models. Extremes. ISSN 1386-1999 (In Press)

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Conditionally specified models are often used to model complex multi- variate data. Such models assume implicit structures on the extremes. So far, there exist no methodology for calculating extremal characteristics of conditional models as 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 calculate implicit assumptions on the extremes of this class of models. In particular, these tools allow us to approximate the distribu- tion of the tail of Y and the cofficient of asymptotic independence eta 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 (2004), and we prove that there exist models that asymptot- ically follow the same conditional representation but have different eta.

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21 Oct 2022 12:55
In Press
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22 Nov 2022 11:58