报 告 人：周望 教授
报告题目：Testing the number of common factors by bootstrapped sample covariance matrix in high-dimensional factor models
报告时间：2023年12月18日（周一下午3：00 )
报告地点：江苏师范大学数学与统计学院学术报告厅（静远楼1506室）
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
周望，2004年7月起在新加坡国立大学统计系任教，并于2009年1月获终身教授。现为新加坡国立大学教授。主要研究方向为: random matrices, SLE, high dimensional statistics。近年来发表有较高学术水平的论文五十多篇。 其中在概率统计学方面的国际公认的顶尖杂志Annals of Statistics, Journal of American Statistical Association, Biometrika, Annals of Probability, Probability Theory and Related Fields, Annals of Applied Probability上发表论文十余篇。2012获得国际统计学会当选成员（Elected Member of International Statistical Institute）。2012年获得新加坡国立大学 “杰出科学家奖”。2005年起主持新加坡政府基金项目十余项。
报告摘要：
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.