Separable sample covariance matrices under elliptical populations with applications

Li, Huiqin; Pan, Guangming; Yin, Yanqing; Zhou, Wang

doi:10.1090/tran/9070

Separable sample covariance matrices under elliptical populations with applications
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by Huiqin Li, Guangming Pan, Yanqing Yin and Wang Zhou

Trans. Amer. Math. Soc.

DOI: https://doi.org/10.1090/tran/9070

Published electronically: April 11, 2024

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Abstract:

This paper is to investigate the spectral properties of separable covariance matrices under elliptical populations. The separable covariance matrix model can handle both cross-row and cross-column correlations thus gain more popularity recently. Under the high-dimensional setting where the dimension $p$ and the sample size $n$ tend to infinity proportionally, we find the limit of the empirical spectral distribution and establish the central limit theorems (CLT) for linear spectral statistics of such kinds of sample covariance matrices. Some applications of our established CLT are also given.

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