On the overestimation of the largest eigenvalue of a covariance matrix

Soufiane Hayou

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arXiv · 1708.03551

On the overestimation of the largest eigenvalue of a covariance matrix

Soufiane Hayou

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Abstract

In this paper, we use a new approach to prove that the largest eigenvalue of the sample covariance matrix of a normally distributed vector is bigger than the true largest eigenvalue with probability 1 when the dimension is infinite. We prove a similar result for the smallest eigenvalue.

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Soufiane Hayou. 2017-08-11. On the overestimation of the largest eigenvalue of a covariance matrix. https://arxiv.org/abs/1708.03551

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