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Math paper details resolvent convergence for sample covariance matrices

By PulseAugur Editorial · [1 sources] ·

This paper investigates the convergence of resolvent matrices for sample covariance matrices with general covariance profiles. The authors establish bounds for the trace of a matrix multiplied by the resolvent, controlled by the Hilbert-Schmidt norm of the matrix. These bounds are dependent on moment conditions of quadratic forms derived from the matrix entries. AI

RANK_REASON This is an academic paper on a mathematical topic related to statistics and machine learning. [lever_c_demoted from research: ic=1 ai=0.7]

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Math paper details resolvent convergence for sample covariance matrices

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  1. arXiv stat.ML TIER_1 English(EN) · Cosme Louart ·

    Resolvent convergence for sample covariance matrices with general covariance profiles and quadratic-form control

    arXiv:2109.02644v4 Announce Type: replace-cross Abstract: We study the resolvent \[ G^z = \left(\frac{1}{n}XX^T - zI_p\right)^{-1}, \qquad z\in\mathbb C,\ \Im(z)>0, \] where $X=(x_1,\ldots,x_n)\in\mathcal M_{p,n}$ is a random matrix with independent, but not necessarily identical…

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