  For factor model, the involved covariance matrix often has no row sparse
structure because the common factors may lead some variables to strongly
associate with many others. Under the ultra-high dimensional paradigm, this
feature causes existing methods for sparse covariance matrix in the literature
not directly applicable. In this paper, for general covariance matrix, a novel
approach to detect these variables that is called the pivotal variables is
suggested. Then, two-stage estimation procedures are proposed to handle
ultra-high dimensionality in factor model. In these procedures, pivotal
variable detection is performed as a screening step and then existing
approaches are applied to refine the working model. The estimation efficiency
can be promoted under weaker assumptions on the model structure. Simulations
are conducted to examine the performance of the new method and a real dataset
is analysed for illustration.
