  In this paper, we establish some new central limit theorems for certain
spectral statistics of a high-dimensional sample covariance matrix under a
divergent spectral norm population model. This model covers the divergent
spiked population model as a special case. Meanwhile, the number of the spiked
eigenvalues can either be fixed or grow to infinity. It is seen from our
theorems that the divergence of population spectral norm affects the
fluctuations of the linear spectral statistics in a fickle way, depending on
the divergence rate.
