报告题目：Rank-based indices for testing independence between two high-dimensional vectors
报告时间：2024年12月 20 日 （星期五）15:00-16:00
报告地点：翡翠湖校区科教楼B座1005
报 告 人：许凯
工作单位：安徽师范大学
主办单位：合肥工业大学经济学院
报告简介：To test independence between two high-dimensional random vectors, wepropose three tests based on the rank-based indices derived from Hoeffding's, Blum-Kiefer-Rosenblatt's and Bergsma-Dassios-Yanagimoto's . 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 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 are sorted in a descending order.
报告人简介：许凯，安徽师范大学教授、博士生导师，博士研究生学历，安徽省数学会和青年统计学家协会理事。主要从事复杂非线性相依关系度量及应用的研究，在Annals of Statistics，Journal of the American Statistical Association，Biometrika、Scandinavian Journal of Statistics、Statistica Sinica、Science China Mathematics等国内外重要学术期刊上发表研究论文40余篇，研究工作得到安徽省高端人才引育行动项目，安徽省自然科学基金优青、青年项目，以及国家自然科学基金面上、青年项目等资助，获第五届安徽省青年数学奖，入选安徽师范大学学科后备人才。
