  Factor modeling is an essential tool for exploring intrinsic dependence
structures among high-dimensional random variables. Much progress has been made
for estimating the covariance matrix from a high-dimensional factor model.
However, the blessing of dimensionality has not yet been fully embraced in the
literature: much of the available data is often ignored in constructing
covariance matrix estimates. If our goal is to accurately estimate a covariance
matrix of a set of targeted variables, shall we employ additional data, which
are beyond the variables of interest, in the estimation? In this paper, we
provide sufficient conditions for an affirmative answer, and further quantify
its gain in terms of Fisher information and convergence rate. In fact, even an
oracle-like result (as if all the factors were known) can be achieved when a
sufficiently large number of variables is used. The idea of utilizing data as
much as possible brings computational challenges. A divide-and-conquer
algorithm is thus proposed to alleviate the computational burden, and also
shown not to sacrifice any statistical accuracy in comparison with a pooled
analysis. Simulation studies further confirm our advocacy for the use of full
data, and demonstrate the effectiveness of the above algorithm. Our proposal is
applied to a microarray data example that shows empirical benefits of using
more data.
