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arXiv · 1511.02711

The necessary and sufficient conditions in the Marchenko-Pastur theorem

Pavel Yaskov
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Abstract

We show that a weak concentration property for quadratic forms of isotropic random vectors ${\bf x}$ is necessary and sufficient for the validity of the Marchenko-Pastur theorem for sample covariance matrices of random vectors having the form $C{\bf x}$, where $C$ is any rectangular matrix with orthonormal rows. We also obtain some general conditions guaranteeing the weak concentration property.

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Pavel Yaskov. 2015-11-09. The necessary and sufficient conditions in the Marchenko-Pastur theorem. https://doi.org/10.1214/16-ecp4748%3B%2010.1007%2Fs10959-017-0767-z

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