Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications

2019/01/23 by Li, Huiqin, Yin, Yanqing, Zheng, Shurong
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1901.07746

Abstract

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 m₁× m₂ dimension, the entries \x_jk, j=1,...,m₁, k=1,...,m₂\ are independent and identically distributed complex variables with zero means and unit variances, \mathbf T_1n is a p× m₁ complex matrix and \mathbf T_2n is an m₂× m₂ Hermitian matrix. We then apply this general central limit theorem to the problem of testing white noise in time series.

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