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The EVA 2023 data competition consisted of four challenges, ranging frominterval estimation for very high quantiles of univariate extremes conditionalon covariates, point estimation of unconditional return levels under a customloss function, to estimation of the probabilities of tail events for low andhigh-dimensional multivariate data. We tackle these tasks by revisiting thecurrent and existing literature on conditional univariate and multivariateextremes. We propose new cross-validation methods for covariate-dependentmodels, validation metrics for exchangeable multivariate models, formulae forthe joint probability of exceedance for multivariate generalized Pareto vectorsand a composition sampling algorithm for generating multivariate tail eventsfor the latter. We highlight overarching themes ranging from model validationat extremely high quantile levels to building custom estimation strategies thatleverage model assumptions.

An utopic adventure in the modelling of conditional univariate and multivariate extremes