報(bào)告人：周望 教授

報(bào)告題目：MULTIPLIER BOOTSTRAP MEETS HIGH-DIMENSIONAL PCA: THE GOOD, THE BAD AND THE MODIFICATION

報(bào)告時(shí)間：2025年11月18日（周二）10:00-11:00

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

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，國(guó)際著名期刊Random Matrices-Theory and Applications的主編。主要研究方向?yàn)? High dimensional statistics，Random matrices, SLE,等。近年來(lái)發(fā)表有高水平論文九十多篇。 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)表論文二十余篇。2005年起主持新加坡政府基金項(xiàng)目十余項(xiàng)。2012獲國(guó)際統(tǒng)計(jì)學(xué)會(huì)當(dāng)選成員（Elected Member of International Statistical Institute）；2021年獲國(guó)際數(shù)理統(tǒng)計(jì)學(xué)會(huì)(IMS)Fellow。

報(bào)告摘要：

In this paper, we examine the feasibility (i.e., both the good advantages and the bad limitations) and the adaptivity (i.e., the potential for beneficial modifications) of employing multiplier bootstrap to analyze the asymptotic distributions of the largest eigenvalues of potentially spiked high-dimensional sample covariance matrices. Our findings and proposed algorithms demon- strate that multiplier bootstrap remains valid, provided the multipliers are ap-propriately chosen and the bootstrap procedures are applied multiple times with suitable corrections.