论文标题
对多元重型分布的极端期望的联合推断
Joint inference on extreme expectiles for multivariate heavy-tailed distributions
论文作者
论文摘要
最初在测试线性回归中误差分布的有条件对称性的背景下引入的预期概念，引起了一种法律不变，连贯且可观的风险措施，该措施在精算和财务风险管理环境中引起了很大的关注。最近的许多论文集中在极端预期风险措施及其风险管理潜力的行为和估计上。然而，几个极端期望的联合推断未被触及。实际上，在有限样本中，即使是边缘极端期望的推断也是一个困难的问题。我们研究了具有重型边缘分布的随机向量的几个极端边缘期望的同时估计。这是在一般的极端依赖模型中完成的，其中重点是边缘之间的成对依赖性。我们使用结果来获得极端预期的准确置信区，以及对几个极端期望的平等的测试。我们的方法在有限样本的仿真研究和实际财务数据中展示。
The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has received a significant amount of attention in actuarial and financial risk management contexts. A number of recent papers have focused on the behaviour and estimation of extreme expectile-based risk measures and their potential for risk management. Joint inference of several extreme expectiles has however been left untouched; in fact, even the inference of a marginal extreme expectile turns out to be a difficult problem in finite samples. We investigate the simultaneous estimation of several extreme marginal expectiles of a random vector with heavy-tailed marginal distributions. This is done in a general extremal dependence model where the emphasis is on pairwise dependence between the margins. We use our results to derive accurate confidence regions for extreme expectiles, as well as a test for the equality of several extreme expectiles. Our methods are showcased in a finite-sample simulation study and on real financial data.
