主题：Estimating Number of Factors by Adjusted Eigenvalues Thresholding
主讲人：郑术蓉（东北师范大学）
主持人：刘一鸣（太阳城集团）
会议时间：2021 年 12 月 31 日（周五）14:00-15:00
会议工具：腾讯会议（ID：270-150-847）
摘要
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. Thus, we propose a tuning-free scale-invariant adjusted correlation thresholding (ACT) method for determining the number of common factors in high-dimensional factor models, taking into account the sampling variabilities and biases of top sample eigenvalues. We also establish the optimality of the proposed ACT method in terms of minimal signal strength and the optimal threshold. Simulation studies lend further support to our proposed method and show that our estimator outperforms competing methods in most test cases.
主讲人简介
郑术蓉，东北师范大学教授，教育部重大人才工程项目特聘教授。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 Sinica, Journal of Multivariate Analysis 《应用概率统计》学术期刊编委。
