We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. The method we utilize for characterizing dependence in the tail is largely nonparametric. The extremes framework enables drawing isolines corresponding to very low exceedance probabilities and may even lie beyond the range of the data; such cases would be problematic for standard nonparametric methods. Furthermore, we extend this method to the case of asymptotic independence and propose a procedure which smooths the transition from hidden regular variation in the interior to the first-order behavior on the axes. We propose a diagnostic plot for assessing the isoline estimate and choice of smoothing, and a bootstrap procedure to visually assess uncertainty.

中文翻译：

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产生二元超出概率等值线的非参数方法

我们提出了一种绘制等值线的方法，该等值线指示针对双变量数据的联合超出概率相等的区域。该方法依赖于二元规则变化，这是一种广泛用于极端情况的依赖框架。我们用于表征尾部相关性的方法主要是非参数的。极限框架允许绘制与极低超标概率相对应的等值线，甚至可能超出数据范围。对于标准的非参数方法，这种情况会成问题。此外，我们将此方法扩展到渐近独立的情况，并提出了一个程序，该程序可平滑从内部隐藏的规则变化到轴上一阶行为的过渡。我们提出了一个诊断图，用于评估等值线估计和平滑选择，