To capture the extremal behaviour of complex environmental phenomena in practice, flexible techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula Utopiversity team to tackle the data challenge of the 2023 Extreme Value Analysis Conference. This data challenge was split into four sections, labelled C1-C4. Challenges C1 and C2 comprise univariate problems, where the goal is to estimate extreme quantiles for a non-stationary time series exhibiting several complex features. We propose a flexible modelling technique, based on generalised additive models, with diagnostics indicating generally good performance for the observed data. Challenges C3 and C4 concern multivariate problems where the focus is on estimating joint extremal probabilities. For challenge C3, we propose an extension of available models in the multivariate literature and use this framework to estimate extreme probabilities in the presence of non-stationary dependence. Finally, for challenge C4, which concerns a 50 dimensional random vector, we employ a clustering technique to achieve dimension reduction and use a conditional modelling approach to estimate extremal probabilities across independent groups of variables.

翻译：为在实际中捕捉复杂环境现象的极端行为，需要灵活的技术来建模尾部特征。本文介绍了兰科普拉乌托维蒂团队为应对2023年极值分析会议数据挑战所采用的多种此类方法。该数据挑战分为四个部分，标记为C1至C4。挑战C1和C2为单变量问题，目标是对呈现多种复杂特征的非平稳时间序列进行极端分位数估计。我们提出基于广义可加模型的灵活建模技术，诊断结果表明该方法对观测数据具有总体良好表现。挑战C3和C4涉及多变量问题，重点在于估计联合极端概率。针对挑战C3，我们提出了多变量文献中现有模型的扩展形式，并利用该框架在存在非平稳依赖关系的情况下估计极端概率。最后，针对涉及50维随机向量的挑战C4，我们采用聚类技术实现降维，并使用条件建模方法估计跨独立变量组的极端概率。