  This paper proposes new estimators of the number of factors for a generalised
factor model with more relaxed assumptions than the strict factor model. Under
the framework of large cross-sections $N$ and large time dimensions $T$, we
first derive the bias-corrected estimator $\hat \sigma^2_*$ of the noise
variance in a generalised factor model by random matrix theory. Then we
construct three information criteria based on $\hat \sigma^2_*$, further
propose the consistent estimators of the number of factors. Finally,
simulations and real data analysis illustrate that our proposed estimations are
more accurate and avoid the overestimation in some existing works.
