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February 2012 Statistical analysis of factor models of high dimension
Jushan Bai, Kunpeng Li
Ann. Statist. 40(1): 436-465 (February 2012). DOI: 10.1214/11-AOS966


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.


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Jushan Bai. Kunpeng Li. "Statistical analysis of factor models of high dimension." Ann. Statist. 40 (1) 436 - 465, February 2012.


Published: February 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1246.62144
MathSciNet: MR3014313
Digital Object Identifier: 10.1214/11-AOS966

Primary: 62H25
Secondary: 62F12

Keywords: factor loadings , factors , High-dimensional factor models , idiosyncratic variances , maximum likelihood estimation , principal components

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.40 • No. 1 • February 2012
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