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

发布时间：2024-11-05 作者：77779193永利官网浏览次数：

Speaker:	周叶青	DateTime:	11月11日上午10：00 - 11：00
Brief Introduction to Speaker: 周叶青，同济大学数学科学学院特聘研究员，博士生导师，国家高层次人才计划青年项目入选者。研究方向为高维数据降维、独立/条件独立检验。研究成果发表在Annals of Statistics、Journal of the American Statistical Association、Journal of Econometrics、Journal of Business & Economic Statistics等期刊上，主持国家自然科学基金面上与青年、上海市自然科学基金面上等项目。		Place:	6号楼二楼报告厅
Abstract: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 τ∗. 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, τ∗ and Pearson’s correlation for bivariate normal random variables. The relationships serve as a basis for power compari...

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