论文标题
关于双变量阿基赛人和极值的有条件收敛性，以及对非参数估计的后果
On weak conditional convergence of bivariate Archimedean and Extreme Value copulas, and consequences to nonparametric estimation
论文作者
论文摘要
从有条件分布的角度来看双变量copulas，并考虑几乎所有条件分布的弱收敛性都会产生弱条件收敛的概念。乍一看，Copulas的这种融合概念似乎太过限制了，以至于没有任何实际重要性 - 实际上，考虑到相应的经验Copulas的样本并不是薄弱地汇总到$ c $的情况下，总体上是概率。然而，在阿基米德·库普拉斯（Archimedean Copulas）的类别和极值copulas的类别中，可以证明标准倾斜收敛和弱条件收敛是等效的。此外，可以证明，每个copula $ c $都是一系列棋盘库copulas的条件限制。在证明了这三个主要结果并指出了一些后果之后，我们概述了最近引入的两个依赖措施以及对阿基马裔和极端价值copulas的非参数估计的一些含义。
Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of convergence for copulas might seem far too restrictive to be of any practical importance - in fact, given samples of a copula $C$ the corresponding empirical copulas do not converge weakly conditional to $C$ with probability one in general. Within the class of Archimedean copulas and the class of Extreme Value copulas, however, standard pointwise convergence and weak conditional convergence can even be proved to be equivalent. Moreover, it can be shown that every copula $C$ is the weak conditional limit of a sequence of checkerboard copulas. After proving these three main results and pointing out some consequences we sketch some implications for two recently introduced dependence measures and for the nonparametric estimation of Archimedean and Extreme Value copulas.
