Detecting independence of random vectors II. Distance multivariance and Gaussian multivariance
Detecting independence of random vectors II. Distance multivariance and Gaussian multivariance
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检测随机向量的独立性 II．
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
R. Schilling
中科院分区：
文献类型：
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作者：
Björn Böttcher;Martin Keller;R. Schilling
我们引入了两个新的措施的依赖性$n \ge 2$随机变量：“距离多变量”和“总距离多变量”。这两种度量都是基于与潜在随机变量的特征函数相关的量的加权L^2 $-距离。他们延长距离协方差（介绍了Szekely，Rizzo和Bakirov）和广义距离协方差（在第一部分介绍）从对随机变量的$n$-tuplets随机变量。我们表明，总距离多变量可以用来检测$n$随机变量的独立性，并有一个简单的有限样本表示的样本点的距离矩阵，其中距离是由一个连续的负定函数。基于我们的理论结果，我们提出了一个测试的独立性的多个随机向量，这是一致的对所有的替代品。
We introduce two new measures for the dependence of $n \ge 2$ random variables: `distance multivariance' and `total distance multivariance'. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic functions of the underlying random variables. They extend distance covariance (introduced by Szekely, Rizzo and Bakirov) and generalized distance covariance (introduced in part I) from pairs of random variables to $n$-tuplets of random variables. We show that total distance multivariance can be used to detect the independence of $n$ random variables and has a simple finite-sample representation in terms of distance matrices of the sample points, where distance is measured by a continuous negative definite function. Based on our theoretical results, we present a test for independence of multiple random vectors which is consistent against all alternatives.
再现核希尔伯特空间的依赖性分析。
DOI：
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发表时间：
2008
期刊：
影响因子：
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作者：
渡辺有祐;福水健次;福水健次;福水健次;福水健次;福水健次;福水健次;福水健次;福水健次;福水健次;福水健次;福水健次
通讯作者：
福水健次