A0511
Title: On statistical analysis of high-dimensional factor models
Authors: Zhigen Gao - Northeast Normal University (China) [presenting]
Abstract: High-dimensional factor models have been applied in many fields. The principal component analysis is a popular estimation method for factor models to compute and provides consistent estimators for common factors and factor loadings. Several contributions are made to the asymptotic properties of the principal components estimates (PCE) of factor models as both the sample size $T$ and the variable dimension $N$ go to infinity. Firstly, bias-adjusted estimates of variance are presented for both common factors and idiosyncratic errors. Secondly, an interesting result is found that the predictor of common factors is also biased with the bias of $O_p(T^{(-1)})$ under the PC, especially for the case that $T$ is relatively small compared with $N$. Meanwhile, the minor modification makes estimates of variance for both common factors and idiosyncratic errors, the predictor of common factors unbiased with a theoretical guarantee. Finally, the asymptotic properties of the PCE are established under a novel proof framework. Simulations are carried out to verify these results.
