講座編號(hào)：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(xué)

講座時(shí)間：2021年04月23日（星期五）下午15:00

講座地點(diǎn)：良鄉(xiāng)校區(qū)數(shù)統(tǒng)樓112室及騰訊會(huì)議，會(huì)議ID：406 145 918 25（入會(huì)密碼 0305）

參加對(duì)象：相關(guān)方向教師及研究生

主辦單位：研究生院

承辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院

主講人簡(jiǎn)介：

張忠占，北京工業(yè)大學(xué)教授，博士生導(dǎo)師，歷任北京工業(yè)大學(xué)數(shù)理學(xué)院院長(zhǎng)，研究生院常務(wù)副院長(zhǎng)。中國(guó)科協(xié)第八、九屆全國(guó)委員會(huì)委員，曾任中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)副理事長(zhǎng)，生物統(tǒng)計(jì)分會(huì)理事長(zhǎng)，教育部統(tǒng)計(jì)學(xué)專(zhuān)業(yè)教學(xué)指導(dǎo)委員會(huì)委員，國(guó)家統(tǒng)計(jì)局專(zhuān)家委員會(huì)委員等。擔(dān)任《數(shù)理統(tǒng)計(jì)與管理》副主編，《生物數(shù)學(xué)學(xué)部》編委，《International Journal of Biomathematics》Editor。從事數(shù)理統(tǒng)計(jì)及其應(yīng)用研究，在國(guó)內(nèi)外學(xué)術(shù)期刊發(fā)表論文120多篇，主持完成國(guó)家自然科學(xué)基金等課題20余項(xiàng)。

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.