主講人：張金廷 新加坡國(guó)立大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系教授

時(shí)間：2022年10月21日13：00

地點(diǎn)：騰訊會(huì)議 815 7887 2599

舉辦單位：數(shù)理學(xué)院

主講人介紹：張金廷教授1988年在北京大學(xué)取得學(xué)士學(xué)位，1991年在中國(guó)科學(xué)院應(yīng)用數(shù)學(xué)所取得碩士學(xué)位， 1999年在美國(guó)北卡萊那大學(xué)教堂山分校取得博士學(xué)位。 張教授曾在哈佛大學(xué)做博士后， 并先后在美國(guó)普林斯頓，羅澤斯特等大學(xué)做高級(jí)訪(fǎng)問(wèn)學(xué)者。張教授現(xiàn)任新加坡國(guó)立大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系終身教授，博士生、博士后導(dǎo)師。他先后培養(yǎng)了十個(gè)碩士，八個(gè)博士以及八個(gè)博士后。他發(fā)表了七十多篇學(xué)術(shù)論文，撰寫(xiě)了兩本統(tǒng)計(jì)專(zhuān)著，以及編撰了一本學(xué)術(shù)論文集。他現(xiàn)任和曾任幾家學(xué)術(shù)期刊的副主編或者編委。他曾是六次大型國(guó)際會(huì)議的組織成員。張金廷教授現(xiàn)在的研究領(lǐng)域包括非參數(shù)統(tǒng)計(jì)，縱向數(shù)據(jù)分析，函數(shù)數(shù)據(jù)分析，高維數(shù)據(jù)分析，等等。

內(nèi)容介紹：We propose a normal-reference test for the two-sample Behrens-Fisher problems for high-dimensional data where the data dimension is very large and even much larger than the sample size. It is shown that the null distribution of the test statistic is the same as that of a chi-square-type mixture which is obtained from the test statistic itself when the null hypothesis holds and when the two samples are normally distributed. The distribution of the chi-square-type mixture can be well approximated by a three-cumulant matched χ2-approximation with the approximation parameters consistently estimated from the data. The asymptotical power of the proposed normal-reference test under a local alternative is established. Two simulation studies demonstrate that in terms of size control, the proposed normal- reference test with the three-cumulant matched χ2-approximation performs well regardless if the data are nearly uncorrelated, moderately correlated, or highly correlated and it performs much better than several existing competitors. A real data example illustrates the proposed normal-reference test.