论文标题
基于副群的下尾概率和上尾概率之间的不对称度量
Copula-based measures of asymmetry between the lower and upper tail probabilities
论文作者
论文摘要
我们提出了基于Copula的基于双变量分布的下尾概率和上尾概率之间的不对称度量。所提出的度量具有简单的形式，并具有一些理想的特性作为不对称的度量。当索引进入其域的边界时，提出的度量的极限可以在Copulas的某些条件下以简单的形式表示。提出了来自副群的样品的样本类似物，并显示了其弱收敛到高斯过程。给出的另一个样本类似物是基于$ \ mathbb {r}^2 $的分布的样本。提出了基于两个样本类似物的间隔估计和非参数测试的简单方法。例如，提出的措施适用于S＆P500和Nikkei225的每日回报。
We propose a copula-based measure of asymmetry between the lower and upper tail probabilities of bivariate distributions. The proposed measure has a simple form and possesses some desirable properties as a measure of asymmetry. The limit of the proposed measure as the index goes to the boundary of its domain can be expressed in a simple form under certain conditions on copulas. A sample analogue of the proposed measure for a sample from a copula is presented and its weak convergence to a Gaussian process is shown. Another sample analogue of the presented measure, which is based on a sample from a distribution on $\mathbb{R}^2$, is given. Simple methods for interval estimation and nonparametric testing based on the two sample analogues are presented. As an example, the presented measure is applied to daily returns of S&P500 and Nikkei225.
