Inferential Theory for Factor Models of Large Dimensions
为大维度因子模型建立推断理论，证明主成分估计的收敛速度和极限分布，适用于大截面和大时间维度，允许相关性和异方差性。
This paper develops an inferential theory for factor models of large dimensions. The principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator (if normality is assumed). We derive the rate of convergence and the limiting distributions of the estimated factors, factor loadings, and common components. The theory is developed within the framework of large cross sections (N) and a large time dimension (T), to which classical factor analysis does not apply. We show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of N and T. The estimated factors and their loadings are generally normal, although not always so. The convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components. These results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions. Stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic. A necessary and sufficient condition for consistency is derived for large N but fixed T.