We propose a model to flexibly estimate joint tail properties by exploiting the convergence of an appropriately scaled point cloud onto a compact limit set. Characteristics of the shape of the limit set correspond to key tail dependence properties. We directly model the shape of the limit set using Bezier splines, which allow flexible and parsimonious specification of shapes in two dimensions. We then fit the Bezier splines to data in pseudo-polar coordinates using Markov chain Monte Carlo, utilizing a limiting approximation to the conditional likelihood of the radii given angles. By imposing appropriate constraints on the parameters of the Bezier splines, we guarantee that each posterior sample is a valid limit set boundary, allowing direct posterior analysis of any quantity derived from the shape of the curve. Furthermore, we obtain interpretable inference on the asymptotic dependence class by using mixture priors with point masses on the corner of the unit box. Finally, we apply our model to bivariate datasets of extremes of variables related to fire risk and air pollution.

翻译：我们提出一种模型，通过利用适当缩放的点云收敛到紧致极限集的性质，灵活估计联合尾部特征。极限集形状的特性对应关键的尾部依赖属性。我们直接使用贝塞尔样条对极限集形状建模，该方法允许在二维空间中以灵活且简约的方式指定形状。随后，我们利用极坐标下角度给定半径的条件似然的极限近似，通过马尔可夫链蒙特卡洛方法将贝塞尔样条拟合至伪极坐标数据。通过对贝塞尔样条参数施加适当约束，确保每个后验样本均为有效的极限集边界，从而可对曲线形状导出的任意量进行直接后验分析。此外，通过使用在单位盒角点处具有点质量的混合先验，我们获得渐近依赖类别的可解释推断。最后，我们将模型应用于与火灾风险和空气污染相关的二元极值数据集。