风险传染涉及任何处理大规模风险的实体。假设（X，Y）表示某个系统中两个分量的风险向量。风险传染的一个相关度量是量化Y的高值对X的影响。这可以通过多种方式来衡量。本文研究了两个这样的测度：量E[max（X-t，0）]| Y > t]称为边际平均超额（MME）以及相关量E[X| Y > t]称为边际预期短缺（MES）。这两个数量都是风险蔓延的指标，在从金融、保险和系统性风险到环境和气候风险的各种应用中都很有用。我们在风险向量（X，Y）的多元正则变差、隐正则变差和渐近尾独立性的假设下工作。许多广泛而有用的模型类满足这些假设。我们提出了几个例子，并推导出MME和MES的阈值t趋于无穷大的渐近行为。我们观察到，虽然我们假设模型中的渐近尾部独立性，但MME和MES在非常一般的条件下收敛到1;这反映了模型中潜在的弱依赖性仍然很重要。除了经验估计的一致性，我们引入了一个外推方法的基础上极值理论估计MME和MES的高阈值t的数据很少。我们表明，这些估计是一致的，并说明我们的方法在模拟和真实的数据集。
英文摘要：
Risk contagion concerns any entity dealing with large scale risks. Suppose (X,Y) denotes a risk vector pertaining to two components in some system. A relevant measurement of risk contagion would be to quantify the amount of influence of high values of Y on X. This can be measured in a variety of ways. In this paper, we study two such measures: the quantity E[max(X-t,0)|Y > t] called Marginal Mean Excess (MME) as well as the related quantity E[X|Y > t] called Marginal Expected Shortfall (MES). Both quantities are indicators of risk contagion and useful in various applications ranging from finance, insurance and systemic risk to environmental and climate risk. We work under the assumptions of multivariate regular variation, hidden regular variation and asymptotic tail independence for the risk vector (X,Y). Many broad and useful model classes satisfy these assumptions. We present several examples and derive the asymptotic behavior of both MME and MES as the threshold t tends to infinity. We observe that although we assume asymptotic tail independence in the models, MME and MES converge to 1 under very general conditions; this reflects that the underlying weak dependence in the model still remains significant. Besides the consistency of the empirical estimators, we introduce an extrapolation method based on extreme value theory to estimate both MME and MES for high thresholds t where little data are available. We show that these estimators are consistent and illustrate our methodology in both simulated and real data sets.
Statistical inference for heavy tailed series with extremal independence
本文考虑平稳时间序列$\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $ h \geq 1 $, conditionally on $ X 0 $ to exceed a threshold tending to infinity, the conditional distribution of $ X h$适当归一化弱收敛到一个非退化分布.在本文中，我们考虑估计的正常化和极限分布。
Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised random vectors, conditioning on an extreme component, where the conditional independence relationships of the random vector are described by a chordal graph. Under mild assumptions, the random vector corresponding to the distribution in the weak limit, termed the tail graphical model, inherits the graphical structure of the original chordal graph. Our theory …
A Transferability Criterion for Null-Optimized Variance Reduction in Cumulant-Based Error-Independence Testing
Cherkasy State Business College（切尔卡瑟州立商业学院）；State Scientific Research Institute of Armament and Military Equipment Testing and Certification（国家武器装备测试与认证科学研究院）；Uzhhorod National University（乌日霍罗德国立大学）
