The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 1 (2012), 436-465.
Statistical analysis of factor models of high dimension
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedasticities, which are jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.
Ann. Statist., Volume 40, Number 1 (2012), 436-465.
First available in Project Euclid: 16 April 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62F12: Asymptotic properties of estimators
Bai, Jushan; Li, Kunpeng. Statistical analysis of factor models of high dimension. Ann. Statist. 40 (2012), no. 1, 436--465. doi:10.1214/11-AOS966. https://projecteuclid.org/euclid.aos/1334581749
- Supplementary material: Supplement to “Statistical analysis of factor models of high dimension”. In this supplement we provide the detailed proofs for Theorems 5.1–5.4 and 6.1. We also give a simple and direct proof that the EM solutions satisfy the first order conditions. Remarks are given on how to make use of matrix properties to write a faster computer program.