Journal
ANNALS OF STATISTICS
Volume 40, Issue 1, Pages 436-465Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-AOS966
Keywords
High-dimensional factor models; maximum likelihood estimation; factors; factor loadings; idiosyncratic variances; principal components
Categories
Funding
- NSF [SES-0962410]
- UIBE [11QD11]
- Divn Of Social and Economic Sciences
- Direct For Social, Behav & Economic Scie [962410] Funding Source: National Science Foundation
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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 heteroskedastic-ities, which re jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.
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