  We consider the estimation of factor model-based variance-covariance matrix
when the factor loading matrix is assumed sparse. To do so, we rely on a system
of penalized estimating functions to account for the identification issue of
the factor loading matrix while fostering sparsity in potentially all its
entries. We prove the oracle property of the penalized estimator for the factor
model when the dimension is fixed. That is, the penalization procedure can
recover the true sparse support, and the estimator is asymptotically normally
distributed. Consistency and recovery of the true zero entries are established
when the number of parameters is diverging. These theoretical results are
supported by simulation experiments, and the relevance of the proposed method
is illustrated by an application to portfolio allocation.
