  In this paper, we propose a computationally simple estimator of the
asymptotic covariance matrix of the Principal Components (PC) factors valid in
the presence of cross-correlated idiosyncratic components. The proposed
estimator of the asymptotic Mean Square Error (MSE) of PC factors is based on
adaptive thresholding the sample covariances of the id iosyncratic residuals
with the threshold based on their individual variances. We compare the nite
sample performance of condence regions for the PC factors obtained using the
proposed asymptotic MSE with those of available extant asymptotic and bootstrap
regions and show that the former beats all alternative procedures for a wide
variety of idiosyncratic cross-correlation structures.
