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科学研究
RESEARCH
Estimating Number of Factors by Adjusted Eigenvalues Thresholding
时间  Datetime
2020-07-30 15:00 — 16:00
地点  Venue
Zoom APP(2)()
报告人  Speaker
郑术蓉
单位  Affiliation
东北师范大学教授
邀请人  Host
王成
备注  remarks
Zoom会议号:990 693 23838 会议密码:342363
报告摘要  Abstract

摘要:Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the eigenvalues of the covariance matrix caused by heterogeneous scales of observed variables, it is not easy to give an accurate  relationship between these eigenvalues and the number of common factors.

To overcome this limitation, we appeal to the correlation matrix and show surprisingly that the number of eigenvalues greater than $1$ of population correlation matrix is the same as the number of common factors under some mild conditions.  To utilize such a relationship, we study the random matrix theory based on the sample correlation matrix in order to correct the biases in estimating the top eigenvalues and to take into account of estimation errors in eigenvalue estimation.  This leads us to propose adjusted correlation thresholding (ACT) 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 methods in terms of minimal signal strength and optimal threshold.  Simulation studies lend further support to our proposed method and show that our estimator outperforms other competing methods in most of our testing cases.



报告人介绍: 郑术蓉,  东北师范大学教授, 研究方向是:大维随机矩阵理论及其在高维数据中的应用。