Inferential theory for factor models of large dimensions.
Inferential theory for factor models of large dimensions.
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DOI：
10.1111/1468-0262.00392
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发表时间：
2003-01-01
期刊：
影响因子：
6.1
通讯作者：
Bai, J
中科院分区：
文献类型：
--
作者：
Bai, J
本文针对大维度因子模型发展了一种推断理论。考虑主成分估计量是因为它易于计算，并且在渐近意义下等同于极大似然估计量（如果假定正态性）。我们推导了估计因子、因子载荷以及共同成分的收敛速度和极限分布。该理论是在大截面（\(N\)）和大时间维度（\(T\)）的框架下发展的，经典因子分析并不适用于此框架。我们表明，估计的共同成分是渐近正态的，其收敛速度等于\(N\)和\(T\)的平方根中的最小值。估计的因子及其载荷一般是正态的，但并非总是如此。估计因子和因子载荷的收敛速度可能比估计的共同成分的收敛速度更快。这些结果是在允许两个维度存在相关性和异方差性的一般条件下获得的。当特质误差是序列不相关且同方差时，可以得到更强的结果。对于大\(N\)但固定\(T\)的情况，推导了一致性的一个充分必要条件。
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.