标题： 极大经验似然估计极值分布的谱测度 显示英文标题

标题： Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution

摘要： 考虑从双变量分布函数$F$的样本，该分布函数属于某个极值分布函数$G$的最大域的吸引域。 这个$G$由两个极值指数和一个谱测度来刻画，后者决定了$F$的尾部相关结构。 多元极值理论中的一个重要问题是关于在$L_p$范数意义下谱测度$\Phi_p$的估计问题。 对于每个$p\in[1,\infty]$，提出了一个用于$\Phi_p$的非参数最大经验似然估计量。 主要的新颖之处在于，这些估计量通过谱测度特征化的矩约束得到保证。 在允许尾部独立性的条件下，证明了估计量的渐近正态性。 此外，我们通过若干理论示例演示了这些条件易于验证。 模拟研究表明，新估计量的性能有了显著提高。 两个案例研究说明了如何在实践中实施这些方法。 显示英文摘要

摘要： Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter determining the tail dependence structure of $F$. A major issue in multivariate extreme-value theory is the estimation of the spectral measure $\Phi_p$ with respect to the $L_p$ norm. For every $p\in[1,\infty]$, a nonparametric maximum empirical likelihood estimator is proposed for $\Phi_p$. The main novelty is that these estimators are guaranteed to satisfy the moment constraints by which spectral measures are characterized. Asymptotic normality of the estimators is proved under conditions that allow for tail independence. Moreover, the conditions are easily verifiable as we demonstrate through a number of theoretical examples. A simulation study shows a substantially improved performance of the new estimators. Two case studies illustrate how to implement the methods in practice.