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Central Limit Theorem for Linear Spectral Statistics of General Separable Sample Covariance Matrices with Applications by Li, Huiqin; Yin, Yanqing; Zheng, Shurong is a scholarly article available to read on EtoBox.

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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.

Author

Li, Huiqin; Yin, Yanqing; Zheng, Shurong

Published

2019

Language

EN