Noise variance estimation in a large-dimensional approximate factor model and its application

This paper focuses on a large-dimensional approximate factor model with a general covariance matrix assumption of the idiosyncratic components when both the cross-section [Formula: see text] and the time dimension [Formula: see text] tend to infinity. First, a bias-corrected estimator for noise variance is proposed using random matrix theory, and its asymptotic normality is also established, which is free of the population distribution of the observations. Second, based on this bias-corrected noise variance estimator, the new information criteria are constructed to determine the number of factors. The consistency of the estimators for the number of factors is also proved as both [Formula: see text] and [Formula: see text] approach infinity. Finally, simulations and real data analysis are conducted to show the superiority and generality of our proposed estimators.