Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
share
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 S_n=1/n T_1n X_n T_2n X_n^* T_1n^* where X_n=(x_jk) is of m_1× 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, T_1n is a p× m_1 complex matrix and T_2n is an m_2× m_2 Hermitian matrix. We then apply this general central limit theorem to the problem of testing white noise in time series.
READ FULL TEXT