AI 中文总结
研究多元极值分析中因变量尾部相关性弱导致估计偏差的问题，提出基于许斯勒 - 赖斯模型的截尾矩估计量，证明其渐近正态性，模拟和实际数据应用表明该估计量在某些情况下偏差更小且拟合尾部相关结构更优。
AI 中文摘要
在多元极值分析中，即使某些风险变量在其他变量同时变大时，其尾部相关性可能很弱。这可能导致基于高阈值超额的极限多元（广义）帕累托分布的估计程序出现偏差。本文考虑许斯勒 - 赖斯多元广义帕累托模型，提出基于基础随机向量下尾截尾版本构建的变差函数矩阵的一阶和二阶矩估计量，并证明其渐近正态性。模拟研究表明在某些情况下它们比经验变差函数估计量偏差更小。将估计量应用于多瑙河流域洪水流量数据和美国航班延误数据，结果显示基于一阶截尾矩估计量的拟合模型隐含的尾部相关结构比基于经验变差函数估计量的更符合数据的经验尾部相关性。
英文摘要
In multivariate extreme value analysis, the tail dependence between some of the risk variables at hand may be weak, even when other variables do tend to become large simultaneously. Weak tail dependence may induce a substantial bias in estimation procedures based on the limiting multivariate (generalized) Pareto distribution of excesses over high thresholds. We consider a Hüsler--Reiss multivariate generalized Pareto model and, motivated by this issue, propose first- and second-order moment estimators of its variogram matrix constructed from a lower-tail-clipped version of the underlying random vector. The asymptotic normality of the proposed estimators is established. We demonstrate by simulation studies that they have lower bias than the empirical variogram estimator in certain cases, particularly when the dependence between components is weak. The estimators are applied to flood discharge data from the Danube river basin and the US flight delay data, showing that the tail dependence structure implied by the fitted model based on the first-order clipped moment estimator aligns more closely with the empirical tail dependence of the data than that based on the empirical variogram estimator.
Comments55pages,24figures
