報 告 人：周望 教授

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

報告時間：2023年12月18日（周一下午3：00 )

報告地點：江蘇師范大學數學與統計學院學術報告廳（靜遠樓1506室）

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

     周望，2004年7月起在新加坡國立大學統計系任教，并于2009年1月獲終身教授。現為新加坡國立大學教授。主要研究方向為: random matrices, SLE, high dimensional statistics。近年來發表有較高學術水平的論文五十多篇。 其中在概率統計學方面的國際公認的頂尖雜志Annals of Statistics, Journal of American Statistical Association, Biometrika, Annals of Probability, Probability Theory and Related Fields, Annals of Applied Probability上發表論文十余篇。2012獲得國際統計學會當選成員（Elected Member of International Statistical Institute）。2012年獲得新加坡國立大學 “杰出科學家獎”。2005年起主持新加坡政府基金項目十余項。

報告摘要：

     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.