In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can exist within both the marginal distributions and dependence structure, resulting in complex data structures. In the context of extremes, few methods have been proposed for modelling trends in extremal dependence, even though capturing this feature is important for quantifying joint impact. Motivated by the increasing dependence of data from the UK Climate Projections, we propose a novel semi-parametric modelling framework for bivariate extremal dependence structures. This framework allows us to capture a wide variety of dependence trends for data exhibiting asymptotic independence. When applied to the climate projection dataset, our model is able to capture observed dependence trends and, in combination with models for marginal non-stationarity, can be used to produce estimates of bivariate risk measures at future time points.
翻译:在许多实际应用中,评估环境变量组合的共同影响对于风险管理和结构设计分析十分重要。当同时考虑这些变量时,在边缘分布和依赖性结构中都可能存在非常态性,从而形成复杂的数据结构。在极端情况下,几乎没有提出建立极端依赖性趋势模型的方法,尽管抓住这一特征对于量化联合影响很重要。我们出于对联合王国气候预测数据日益依赖的考虑,提议为双变量极端依赖性结构建立一个新的半参数建模框架。这一框架使我们能够为显示无适应性独立的数据捕捉多种依赖性趋势。在应用气候预测数据集时,我们的模式能够捕捉观察到的依赖性趋势,并与边缘非常态性模型相结合,可用于对未来时间点的双变量风险计量进行估算。