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Estimating Number of Factors by Adjusted Eigenvalues Thresholding

发布时间:2020-12-14 作者: 浏览次数:
Speaker: 郑术蓉 DateTime: 2020年12月15日(周二)下午20:00-21:00
Brief Introduction to Speaker:

郑术蓉,东北师范大学教授、博士生导师。主要研究方向是: 大维随机矩阵理论及其在高维统计中的应用。曾在Annals of Statistics, Journal of the American Statistical Association, Biometrika等统计学期刊上发表多篇跟大维随机矩阵理论有关的学术论文。现任Statistica SinicaJournal of Multivariate Analysis、《应用概率统计》学术期刊编委。曾主持国家自然科学基金委优秀青年科学基金,入选教育部新世纪优秀人才支持计划等。

 

Place: 腾讯会议(会议号请联系左国新老师索取)
Abstract:Determining the number of common factors is an important and practical topic in high-dimensional factor models. The existing literature is mainly based on the eigenvalues of the covariance matrix. Owing to the incomparability of the eigenvalues of the covariance matrix caused by the heterogeneous scales of the observed variables, it is not easy to find an accurate relationship between these eigenvalues and the number of common factors. To overcome this limitation, we appeal to the correlation matrix and demonstrate, surprisingly, that the number of eigenvalues greater than $1$ of the population correlation matrix is the same as the number of common factors under certain mild conditions. To utilize such a relationship, we study random matrix theory based on the sample correlation matrix in order to correct biases in estimating the top eigenvalues and to take into account of estimation errors in eigenvalue estimation.