Symmetric rank covariances: a generalized framework for nonparametric measures of dependence
Symmetric rank covariances: a generalized framework for nonparametric measures of dependence
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DOI：
10.1093/biomet/asy021
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发表时间：
2018-09-01
期刊：
影响因子：
2.7
通讯作者：
Meinshausen, N.
中科院分区：
文献类型：
--
作者：
Weihs, L.;Drton, M.;Meinshausen, N.
测试两个随机向量是否独立的需要已经产生了许多相互竞争的依赖性度量。我们专注于非参数的措施，是不变的严格增加的转换，如肯德尔的tau，Hoeffding的D，和Bergsma-Dassios符号协方差。每一个都表现出对称性，这些对称性从它们的定义中并不明显。使这些对称明确，我们定义了一类新的多元非参数的依赖措施，我们称之为对称秩协方差。这个新的类概括了上述措施，并导致自然的Bergsma-Dassios符号协方差的多变量扩展。对称秩协方差估计无偏使用U-统计，我们证明了计算效率和大样本行为的结果。我们开发的算法，他们的计算包括，据我们所知，第一个有效的算法Hoeffding的D统计在多变量设置。
The need to test whether two random vectors are independent has spawned many competing measures of dependence. We focus on nonparametric measures that are invariant under strictly increasing transformations, such as Kendall's tau, Hoeffding's D, and the Bergsma-Dassios sign covariance. Each exhibits symmetries that are not readily apparent from their definitions. Making these symmetries explicit, we define a new class of multivariate nonparametric measures of dependence that we call symmetric rank covariances. This new class generalizes the above measures and leads naturally to multivariate extensions of the Bergsma-Dassios sign covariance. Symmetric rank covariances may be estimated unbiasedly using U-statistics, for which we prove results on computational efficiency and large-sample behaviour. The algorithms we develop for their computation include, to the best of our knowledge, the first efficient algorithms for Hoeffding's D statistic in the multivariate setting.