统计与数据科学系系列学术报告之四百一十二期

时间：2023年11月16日（周四）15:00-16:00

地点：史带楼503室

主持人：复旦大学管理学院统计与数据科学系张新生教授

报告人：Professor Zhou Wang Department of Statistics and Applied Probability, National University of Singapore

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

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.

个人简介：Professor Zhou Wang is mainly engaged in the theoretical and applied research of statistics, especially in the research of high-dimensional data estimation, high-dimensional data testing, data dimension reduction and large-dimensional data stochastic matrix. More than 80 high-level articles have been published, many of which are published in top journals in the field of statistics and probability science, such as: Annals of Statistics, Journal of American Statistical Association, Biometrika, Annals of Probability, Probability Theory and Related Fields, Annals of Applied Probability. Some articles have been cited by many scholars. Professor Zhou Wang has presided over many projects of the National Natural Science Foundation of Singapore and has been invited to make conference reports and invitation reports at many international conferences. He is now the editor-in-chief of RMTA, IMS Fellow.