讲座编号：jz-yjsb-2021-y007

讲座问题：Testing independence of functional variables by angle covariance

主 讲 人：张忠占 北京工业大学

讲座时间：2021年04月23日（星期五）下昼15:00

讲座所在：良乡校区数统楼112室及腾讯聚会，聚会ID：406 145 918 25（入会密码 0305）

加入工具：相关偏向西席及研究生

主理单位：研究生院

承办单位：数学与统计学院

主讲人简介：

张忠占，北京工业大学教授，博士生导师，历任北京工业大学数理学院院长，研究生院常务副院长
。中国科协第八、九届天下委员会委员，曾任中国现场统计研究会副理事长，生物统计分会理事长，教育部统计学专业教学指导委员会委员，国家统计局专家委员会委员等
。担当《数理统计与治理》副主编，《生物数学学部》编委，《International Journal of Biomathematics》Editor
。从事数理统计及其应用研究，在海内外学术期刊揭晓论文120多篇，主持完成国家自然科学基金等课题20余项
。

主讲内容：

In this talk,We propose a new nonparametric independence test for two functional random variables.The test is based on a new dependence metric,the so-called angle covariance,which fully characterizes the independence of the random variables and generalizes the projection covariance proposed for random vectors.The angle covariance has a number of desirable properties,including the equivalence of its zero value and the independence of the two functional variables, and it can be applied to any functional data without finite moment conditions.We construct a V-statistic estimator of the angle covariance,and show that it has a Gaussian chaos limiting distribution under the independence null hypothesis and a normal limiting distribution under the alternative hypothesis.The test based on the estimated angle covariance is consistent against all alternatives and easy to be implemented by the given random permutation method.Simulations show that the test based on the angle covariance outperforms other competing tests for functional data.