Estimating Number of Factors by Adjusted Eigenvalues Thresholding
By Jianqing Fan, Jianhua Guo, Shu-rong Zheng. Journal of the American Statistical Association, 2019
106 citations recorded by the source corpus.
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 use such a relationship, we study random matrix theory based on the sample correlation matrix 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. Supplementary materials for this article are available online.
Subfields: Radiology, Nuclear Medicine and Imaging, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e825cb86e7d42c59c6ca939e6d93f0204ceb0a17
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In Radiology, Nuclear Medicine and Imaging
In Statistics and Probability
Citations in the corpus
- Statistical Inference for High-Dimensional Matrix-Variate Factor Models (2020, background): “Model (1.1) can be seen as a generalization of the vector factor model (Bai and Ng, 2002; Bai, 2003; Fan et al., 2013; Chang et al., 2015; Fan et al., 2021, 2020) to matrix-variate data.”