论文标题
距离协方差的基本处理
A Basic Treatment of the Distance Covariance
论文作者
论文摘要
Székely等人的距离协方差。 [23]以及Székely和Rizzo [21]是多元随机变量集之间的有力依赖性的强大度量，其至关重要的特征在且仅当集合相互独立时等于零。因此，距离协方差可以应用于多元数据，以检测变量集之间的非线性关联的任意类型。我们在本文中提供了距离协方差的基本，尽管严格的介绍性处理。我们的调查产生了一种方法，即使在高级本科或初级研究生级别的数学统计课程中，也可以用作呈现此重要和及时主题的基础。
The distance covariance of Székely, et al. [23] and Székely and Rizzo [21], a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually independent. Hence the distance covariance can be applied to multivariate data to detect arbitrary types of non-linear associations between sets of variables. We provide in this article a basic, albeit rigorous, introductory treatment of the distance covariance. Our investigations yield an approach that can be used as the foundation for presentation of this important and timely topic even in advanced undergraduate- or junior graduate-level courses on mathematical statistics.
