講座編號：jz-yjsb-2021-y007

講座題目：Testing independence of functional variables by angle covariance

主 講 人：張忠占 北京工業大學

講座時間：2021年04月23日（星期五）下午15:00

講座地點：良鄉校區數統樓112室及騰訊會議，會議ID：406 145 918 25（入會密碼 0305）

參加對象：相關方向教師及研究生

主辦單位：研究生院

承辦單位：數學與統計學院

主講人簡介：

張忠占，北京工業大學教授，博士生導師，歷任北京工業大學數理學院院長，研究生院常務副院長。中國科協第八、九屆全國委員會委員，曾任中國現場統計研究會副理事長，生物統計分會理事長，教育部統計學專業教學指導委員會委員，國家統計局專家委員會委員等。擔任《數理統計與管理》副主編，《生物數學學部》編委，《International Journal of Biomathematics》Editor。從事數理統計及其應用研究，在國內外學術期刊發表論文120多篇，主持完成國家自然科學基金等課題20余項。

主講內容：

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.