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Models for extreme values are generally derived from limit results, which aremeant to be good enough approximations when applied to finite samples.Depending on the speed of convergence of the process underlying the data, theseapproximations may fail to represent subasymptotic features present in thedata, and thus may introduce bias. The case of univariate maxima has beenwidely explored in the literature, a prominent example being the slowconvergence to their Gumbel limit of Gaussian maxima, which are betterapproximated by a negative Weibull distribution at finite levels. In thecontext of subasymptotic multivariate extremes, research has only dealt withspecific cases related to componentwise maxima and multivariate regularvariation. This paper explores the conditional extremes model (Heffernan andTawn, 2004) in order to shed light on its finite-sample behaviour and to reducethe bias of extrapolations beyond the range of the available data. We identifysecond-order features for different types of conditional copulas, and obtainresults that echo those from the univariate context. These results suggestpossible extensions of the conditional tail model, which will enable it to befitted at less extreme thresholds.

Penultimate Analysis of the Conditional Multivariate Extremes Tail Model