Statistical analysis of factor models of high dimension

The Annals of Statistics · 2012 · Volume 40 · Issue 1

Abstract

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.

Keywords

62F12, 62H25, factor loadings, factors, High-dimensional factor models, idiosyncratic variances, maximum likelihood estimation, principal components

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