题目：Rank-based indices for testing independence between two high-dimensional vectors

报告人：许凯

  摘要：To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's $D$, Blum-Kiefer-Rosenblatt's $R$ and Bergsma-Dassios-Yanagimoto's $\tau^{\ast}$. Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions   diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between $D$, $R$,  $\tau^*$ and Pearson's correlation for bivariate normal random variables. The relationships serve as a basis for power comparison. Our theoretical results show that under a Gaussian equicorrelation alternative, (i) the proposed tests are superior to the two classic distance covariance/correlation based tests if the components of random vectors have very different scales; (ii) the  asymptotic  efficiency of the proposed tests based on $D$, $\tau^*$ and $R$ are sorted in a descending order.

  简介：许凯副教授，2018年博士毕业于上海财经大学，现任职于安徽师范大学数学与统计学院。主要从事统计推断及相关领域的研究工作，特别在复杂非线性相依数据和复杂高维数据的研究方面取得了一系列突出成果。在统计学领域国际顶级期刊《The Annals of Statistics》、《Biometrika》、《Journal of the American Statistical Association》以及权威期刊《Statistica Sinica》、《中国科学: 数学》等上发表研究论文近30篇。

 报告地点： #腾讯会议：646-275-533

 报告 时间：4月24日（周三）下午1：30

  联系人：郭文雯