Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
  In this paper, we consider the separable covariance model, which plays an
important role in wireless communications and spatio-temporal statistics and
describes a process where the time correlation does not depend on the spatial
location and the spatial correlation does not depend on time. We established a
central limit theorem for linear spectral statistics of general separable
sample covariance matrices in the form of $\mathbf S_n=\frac1n\mathbf
T_{1n}\mathbf X_n\mathbf T_{2n}\mathbf X_n^*\mathbf T_{1n}^*$ where $\mathbf
X_n=(x_{jk})$ is of $m_1\times m_2$ dimension, the entries $\{x_{jk},
j=1,...,m_1, k=1,...,m_2\}$ are independent and identically distributed complex
variables with zero means and unit variances, $\mathbf T_{1n}$ is a $p\times
m_1 $ complex matrix and $\mathbf T_{2n}$ is an $m_2\times m_2$ Hermitian
matrix. We then apply this general central limit theorem to the problem of
testing white noise in time series.
