论文标题
用于功能数据的经验尾巴
Empirical tail copulas for functional data
论文作者
论文摘要
对于最大稳定分布吸引域中的多元分布，尾巴管道和稳定的尾部依赖函数是捕获上尾依赖性的等效方法。这些功能的经验版本是基于等级的估计量，其膨胀估计误差已弱化为高斯过程，该过程的结构与经验copula过程的弱极限相似。我们通过建立尾巴配件的估计器的渐近正态性，将此多变量结果扩展到连续的功能数据，在最多$ d $点的所有有限子集（固定$ d $固定）上均匀。提出了测试尾部副柱平稳性的应用程序。得出结果的主要工具是所有$ d $变量的尾巴经验过程的均匀渐近正态性。主要结果的证明是非标准。
For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to continuous functional data by establishing the asymptotic normality of the estimators of the tail copula, uniformly over all finite subsets of at most $D$ points ($D$ fixed). An application for testing tail copula stationarity is presented. The main tool for deriving the result is the uniform asymptotic normality of all the $D$-variate tail empirical processes. The proof of the main result is non-standard.
