About limiting spectral distributions of block-rescaled empirical covariance matrices

Gilles Mordant

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arXiv · 2201.07621

About limiting spectral distributions of block-rescaled empirical covariance matrices

Gilles Mordant

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Abstract

We establish that the limiting spectral distribution of a block-rescaled empirical covariance matrix is an arcsine law when the ratio between the dimension and the underlying sample size converges to 1 and when the samples corresponding to each block are independent. We further propose a conjecture for the cases where the latter ratio converges to a constant in the unit interval.

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Gilles Mordant. 2022-01-19. About limiting spectral distributions of block-rescaled empirical covariance matrices. https://arxiv.org/abs/2201.07621

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