Limiting spectral distribution for large sample covariance matrices with graph-dependent elements

Pavel Yaskov

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arXiv · 2105.09625

Limiting spectral distribution for large sample covariance matrices with graph-dependent elements

Pavel Yaskov

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Abstract

We obtain the limiting spectral distribution for large sample covariance matrices associated with random vectors having graph-dependent entries under the assumption that the interdependence among the entries grows with the sample size n. Our results are tight. In particular, they give necessary and sufficient conditions for the Marchenko-Pastur theorem for sample covariance matrices with m-dependent orthonormal elements when m = o(n).

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Pavel Yaskov. 2021-05-20. Limiting spectral distribution for large sample covariance matrices with graph-dependent elements. https://arxiv.org/abs/2105.09625

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