报告时间：2018年12月26日10:00-11:00

报告地点：主楼1214 会议室

报告人：许王莉 教授

主持人：郭永江

报告人简介：

中国人民大学统计学院，教授，博士生导师。2006年毕业于中国科学院数学与系统科学研究院应用所概率论与数理统计专业，目前是中国现场统计研究会生存分析分会副秘书长、国际生物统计学会中国分（IBS-CHINA）青年理事，众多国内外统计学术期刊的审稿专家，现任中国人民大学统计学教授，生物统计系主任。近年来一直从事模型拟合优度检验，高维数据分析，随机缺失数据，两阶段抽样数据以及纵向数据分析等方面的统计推断研究。先后承担了新世纪优秀人才计划，“北京市科技新星计划”，国家自然科学面上基金，国家自然科学青年基金和教育部人文社科基金等多项科研课题，在统计学国际一流期刊发表论文40余篇，并在科学出版社合作出版《非参数蒙特卡洛检验及其应用》和单著《缺失数据的模型检验及其应用》。

报告摘要：

Test of independence between random vectors $X$ and $Y$ is an essential task in statistical inference.

One type of testing methods is based on the minimal spanning tree of variables $X$ and $Y$. The main idea is to generate the minimal spanning tree for one random vector $X$, and for each edges in minimal spanning tree, the corresponding rank number can be calculated based on another random vector $Y$. The resulting test statistics are constructed by these rank numbers. However, the existed statistics are not symmetrical tests about the random vectors $X$ and $Y$ such that the power performance from minimal spanning tree of $X$ is not the same as that from minimal spanning tree of $Y$. In addition, the conclusion from minimal spanning tree of $X$ might conflict with that from minimal spanning tree of $Y$. In order to solve this problem, we propose several symmetrical independence tests for $X$ and $Y$. The exact distributions of test statistics are investigated when the sample size is small. For larger sample size, the calculation is too complicated and a permutation method is introduced for getting critical values of the statistics. Compared with the existing methods, our proposed methods are more efficient demonstrated by numerical analysis.