報(bào) 告 人：鄭術(shù)蓉 教授

報(bào)告題目：Large separable sample covariance matrices: joint CLT for linear spectral statistics and its applications

報(bào)告時(shí)間：2023年10月14日（周六上午9：30 )

報(bào)告地點(diǎn)：江蘇師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院學(xué)術(shù)報(bào)告廳（靜遠(yuǎn)樓1506室）

主辦單位：數(shù)學(xué)研究院、數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

     鄭術(shù)蓉，東北師范大學(xué)教授。主要從事大維隨機(jī)矩陣?yán)碚摷案呔S統(tǒng)計(jì)分析的研究。曾在Annals of Statistics, JASA, Biometrika等統(tǒng)計(jì)學(xué)重要學(xué)術(shù)期刊上發(fā)表多篇學(xué)術(shù)論文和主持多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目等?，F(xiàn)任Annals of Statistics、Statistica Sinica、Journal of Multivariate Analysis等學(xué)術(shù)期刊編委。

報(bào)告摘要：

     This paper studies a group of correlated separable sample covariance matrices which share a latent random matrix but have distinct spatial-temple covariance structures. The entries of the random matrix can be either independent and identically distributed or elliptically correlated across rows. A joint central limit theorem for linear spectral statistics of such covariance matrices is established in high-dimensional frameworks. By utilizing this general result, we extend two classical likelihood ratio tests to high-dimensional situations, including the significance test in a multivariate linear regression and the test for the equality of several covariance matrices.