報(bào) 告 人：周望 教授

報(bào)告題目：Testing the number of common factors by bootstrapped sample covariance matrix  in high-dimensional factor models

報(bào)告時(shí)間：2023年12月18日（周一下午3：00 )

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

報(bào)告人簡(jiǎn)介：

     周望，2004年7月起在新加坡國(guó)立大學(xué)統(tǒng)計(jì)系任教，并于2009年1月獲終身教授?，F(xiàn)為新加坡國(guó)立大學(xué)教授。主要研究方向?yàn)? random matrices, SLE, high dimensional statistics。近年來(lái)發(fā)表有較高學(xué)術(shù)水平的論文五十多篇。 其中在概率統(tǒng)計(jì)學(xué)方面的國(guó)際公認(rèn)的頂尖雜志Annals of Statistics, Journal of American Statistical Association, Biometrika, Annals of Probability, Probability Theory and Related Fields, Annals of Applied Probability上發(fā)表論文十余篇。2012獲得國(guó)際統(tǒng)計(jì)學(xué)會(huì)當(dāng)選成員（Elected Member of International Statistical Institute）。2012年獲得新加坡國(guó)立大學(xué) “杰出科學(xué)家獎(jiǎng)”。2005年起主持新加坡政府基金項(xiàng)目十余項(xiàng)。

報(bào)告摘要：

     This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under the  high-dimensional factor structure.We provide asymptotic distributions for the top  eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits via proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by order statistics of bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. According to the simulations and a real data example, the proposed methods are the only ones performing reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details  contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions. This is joint with Yu Long and Zhao Peng.