The EVA 2023 data competition consisted of four challenges, ranging from interval estimation for very high quantiles of univariate extremes conditional on covariates, point estimation of unconditional return levels under a custom loss function, to estimation of the probabilities of tail events for low and high-dimensional multivariate data. We tackle these tasks by revisiting the current and existing literature on conditional univariate and multivariate extremes. We propose new cross-validation methods for covariate-dependent models, validation metrics for exchangeable multivariate models, formulae for the joint probability of exceedance for multivariate generalized Pareto vectors and a composition sampling algorithm for generating multivariate tail events for the latter. We highlight overarching themes ranging from model validation at extremely high quantile levels to building custom estimation strategies that leverage model assumptions.

翻译：EVA 2023数据竞赛包含四项挑战：从基于协变量的单变量极值极高分位数区间估计、自定义损失函数下无条件重现水平的点估计，到低维与高维多变量数据尾部事件概率的估计。我们通过重新审视现有关于条件单变量与多变量极值的文献来应对这些任务。针对协变量依赖模型，我们提出新的交叉验证方法；针对可交换多变量模型，提出验证指标；针对多变量广义帕累托向量，推导出超越联合概率公式，并设计一种用于生成多变量尾部事件的组合抽样算法。我们重点阐述了从极高分位数水平的模型验证到利用模型假设构建定制化估计策略等贯穿性主题。