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(yè)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(xiāng)校區(qū)數(shù)統(tǒng)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(shù)學與統(tǒng)計學院

主講人簡介：

張忠占，北京工業(yè)大學教授，博士生導師，歷任北京工業(yè)大學數(shù)理學院院長，研究生院常務副院長。中國科協(xié)第八、九屆全國委員會委員，曾任中國現(xiàn)場統(tǒng)計研究會副理事長，生物統(tǒng)計分會理事長，教育部統(tǒng)計學專業(yè)教學指導委員會委員，國家統(tǒng)計局專家委員會委員等。擔任《數(shù)理統(tǒng)計與管理》副主編，《生物數(shù)學學部》編委，《International Journal of Biomathematics》Editor。從事數(shù)理統(tǒng)計及其應用研究，在國內(nèi)外學術期刊發(fā)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(nèi)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.